MKTG 4074 (Data-Driven) Notes

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Apr 3, 2024

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1/18 - Basic Stats Scales: Discrete (nominal + ordinal) vs Continuous (interval) Chi-squared test “In buckets” like 15-20 min, not exact numbers = discrete Steps in Hypothesis Testing (null = Ho , alt = Ha) Compare test stat to critical value
Critical value → alpha/signif level (.01,.005,.1) + degrees of freedom + one-tail or two-tail test Test Relationship between Variables Cross-tab (chi-square test) – discrete Measure observed data, and what’s the expected number what should the numbers be Null = no correlation Alt= there is a relationship Example (chi=squared test) Likelihood to donate - very likely or not likely likelihood of pet ownership- yes or no
Sample size = 329 Expected Probability of donation = 253/329 = 77% Likely and Yes = 150 * probability above = 115 (Row total x column total) / sample size Subtract 115 from row total to find Not Likely and Yes = 35 Subtract from column total too Compute chi-square stat = (observed - expected)^2 ) / expected Reject the null hypothesis if absolute value of test stat > critical value
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Example 2 R D I M: 180 180 40 F: 270 270 60 (Row Total x Column total) / sample size = 40 x^2 stat = 16.2 > 5.99 Reject the null hypothesis at .05 significance level There is a relationship between voting preferences and gender (males vote republican) Steps for Chi-square Test
Steps 1. Make observed table 2. Make the expected table 3. Compute x^2 stat 4. Make conclusion Exercise 1 Now suppose that an additional question revealed that of the 102 respondents with a college degree, 70 indicated they were very likely to donate. Determine whether college degree and likelihood of donation are associated (i.e. not independent) at 0.01 significance level (critical value is 6.64). T-Test (comparing 2 sample means) One Continuous and One Discrete Example
Avg # times/month std dev sample size W/Kids 5 2 55 W/ out kids 3 1 45 Ho = avg # times = avg # times Ha = avg # times > avg # times
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Bigger families w/ kids shop more often than people w/ not kids T-stat > critical value Significance = allows you to generalize “make inferences” to wider population
H0 Likability of A is equal to avg likability of Ad B Ha Likability is greater with A than B > one tailed test not equal two tailed test Exercise 4: Campaign Targeting Avg # Cans Std Dev N Age 18-29 3 3 60 Age 30+ 5 2 50 H0: avg # of cans of 18-29 will be equal to avg consumption of 30+ (no relationship) Ha: the avg # of cans for 30+ are greater than avg # of cans for 18-29 (based on the pattern we see in data, 5 cans > 3)
(3-2) —--- sq(3^2 / 60) + 2^2 / 50) → 4.17 Always use absolute value for total 4.17 > 1.65 Reject the null hypothesis, Conclusion: people 30+ drink more coke than 18-29, so target people 18-29 to increase their consumption Word of Caution - When the rejection criteria is not met, we never “accept” the null hypothesis. Instead, we say, there is insufficient evidence to reject the null hypothesis. Both are continuous, use Correlation testing The degree to which two variables have a tendency to vary together – Can be positive or negative – Range: −1 to +1, 0 means no linear correlation - Ex. the more you study, the better you do on the exam - Outliers (ex. Extreme observations) can seriously affect r - Remove outliers r = correlation coefficient - Only indicate linear covariation
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Spurious Correlation: correlation does not equal causation Testing the Significance of Correlation H0= no relationship / H1= Correlation Example
Conclusion: the bigger a family size, the more frequently they shop at Costco Family size shopping frequency test type Family w/ or w/out kids # times/month t-test Family w/ or w/out kids whether they shop at Costco or not chi-squared # of people/HH # times/month Correlation, r, t-test Is r = 0, or not 0 1/23- Excel – What percentage of sales occurs at each store? – What percentage of sales occurs during each month? – How much revenue does each product generate? Always start analysis with: 1. Plots 2. Summary / descriptive statistics 1/25 - Hypothesis Testing w/ Excel Chi-Squared = pivot table, then chi-test function (actual, expected) → p-value reject NULL if p-value < a H0: no relationship H1: there is a relationship T-Test = 2 sample unequal variances in Excel toolpak → t-stat, critical value, p value Split the continuous variable into 2 columns based on discrete variable Two-tail test = stricter, H0: equal | H1: Not equal Correlation = correlation coefficient ®, t-test (is r significant), use correlation function on toolpack to get correlation matrix
2/1 - Linear Regression Multiple Regression - Attempts to explain a metric variable of interest, called the dependent variable, from a set of predictor variables, called the independent variable - Uses linear additive relation between the dependent and independent variables - Examples - Do prices and promotions affect sales? If so, how? - How to forecast box office revenue of a new movie based on the gross revenues of various past movies? Predictions Sales / outcome = Key Points - Determine whether the independent variables explain a significant variation in the dependent variable: whether a relationship exists - Determine how much of the variation in the dependent variable can be explained by the independent variable: strength of the relationship - Control for other independent variables when evaluating the contributions of a specific variable or set of variables. Marginal Effect - Forecast/Predict the values of the dependent variable - Use regression results as inputs to additional computations : optimal pricing, promotion, time to launch a product (ex. Conjoint analysis’s backend analysis) Linear Model Population Regression Sample regression
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B = coefficients Price + E Right side of equation are things company can change (price) If vertical line = variation in sales, but not in price If horizontal line = variation in price, but not in sales Assumptions of Linear Model To get unbiased data, so find out what assumptions are/if they violate The error term (E) is well behaved - Follows normal distribution E ~ N (o, omega ^2) - Constant variance - Independence: correlations between X variables and the error term are all zero, i.e. corr(Xk,E) = 0 for all k - Endogeneity Problem = something is error term is correlated with independent variable, will cause problems to estimates on Betas Violations of these assumptions will affect the accuracy and statistical significance of the estimates
Significance Tests of Regression Coefficients - Weather or not Betas are 0 or not 0 (are correlation coefficients 0) - Use T-Test Excel Example: - What is the impact of familiarity with internet (7-point scale, 1=very unfamiliar, 7=very familiar) on Internet usage (hours per week)? R Square: familiarity alone can explain almost 71% of variation in internet usage R = corr(iusage, familiarity)
r^2 = R^2 (R Square from excel stat) - Only true for bivariate regression (only 1x) Goodness-of-Fit: R-square - How well linear line fits with data Familiarity with internet • Attitude toward internet(iattitude) and technology (tattitude) • 7-point scales How do familiarity and attitude affect Internet usage?
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Omnibus F-Test - Testing if at least one of the Betas is significant - Only useful when you have more than 1 independent variable
Swap “tattitude” and “iattitude” (column E and F) - What happens when we remove “iattitude” from the regression model? R^2 increases when you have more independent variables - Adjusted R square can see if increase in R^2 is significant or just noise Partial F-Test - Smaller Model 1 (less x variables) has to be nested in Model 2 (more independent variables) - Nested: Variables in model 1 have to be in Model 2 (familiarity, etc.) H0: Model 1 is preferred H1: Model 2 is preferred Compute F-Stat = numerator = diff w/ R^2 / Q = diff of x variables between models K = # of independent variables in bigger model - Thus, the iattitude does not need to be included
2/6 - Linear Regression Part 2 - Whether a relationship exists? - p -value of each individual B (p-value < alpha) - Strength of relationship? - Individual factor - Interpretation of B (a unit change in x → B units change in y) - Overall regression - R Square (use Omnibus F-Test → excel output “Significant F” = p- value associated with F-Test, smaller than .05 than overall regression is sig) - What is the Marginal Effect? - Interpretation of B, then hold everything else constant Regression with Categorical Variables - What is X is a categorical variable? - Ex. gender, income brackets, whether product is on promo or not - Cannot directly use them in regression - Code them as dummy variables (take value of 0 or 1) - What is the dependent variable Y is a categorical variable (left of =)? - A different regression (logistic regression) Regression Model:
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1 = yes, and 2 = no → 1 = yes, 0= no Multicollinearity Problem - Highly correlated variables Solution - Do not include all the Xs that are highly correlated - One of them is enough - Run a regression using one of the Xs as dependent variable on the others Error term at end of equation - Captures everything that we don’t observe in data that might affect revenue (independent variable left of = sign) 1. Follows normal distribution E ~ N (o, omega ^2) - Make histogram 2. Constant variance - Scatter plot between residue and predicted y (predicted gross rev)
3. Independence: correlations between X variables and the error term are all zero, i.e. corr(Xk,E) = 0 for all k - Scatter plot between residuals and error term (each of x variables) - Should be random (flat trendline) Residual Diagnostics - Histogram plot of the residuals (or Normal QQ plot): check if it is normally distributed - Scatter plot of fitted value (i.e. predicted ) vs. residuals: check if there is any 𝑌 relationship - Scatter plots of residuals vs. independent variables to check independence: randomly scattered around 0 Look at Before Running Regression Analysis - Do charts/plots to help decide what model to run - Distribution of outcome (revenue), does it follow normal distribution = make histogram Never take log on discrete variable - Want linear relationship with scatter plots w/ log(variable) - Switch x and y for scatter plot = see y on vertical axis and x on the horizontal axis, how changing x is going to change y - First selected column in y axis, second is x Log(revenue) = B0 + B1 log(FB) + B2 log(budget) + B3 log(IMDB) + B4 Action + B5 Drama Log Transformation - Capturing non-linear effects - Often the phenomenon of interest is skewed, or the relationship between variables is non- linear - Transform variables using natural log 1 unit change in x → B (coefficient) unit change in Y - w/ log it’s 1% change in X → B% change in Y (log = percentage change) - Equation predicting log(revenue)
- For Dummy variables (drama, comedy) Exp(B) - 1 → change to whole % (.24→24%) - Diff in outcome of avg between dummy group and the reference group Semi-log - log(y) = Bo + B1X + E - Take log on y, not the x (continuous) - If Beta is small (<0.1) then Beta is seen as 1 unit change in X is 100xB% change in Y B = 0.06 → .06 * 100 = 6% 2/20 - Logistic Regression Exam 1 - Can use excel for some parts (t-test, chi-squared) - No regression analysis on our own - Will give output, and answer questions based on output Forecasting/predicting the value of Y - Significant or not, use coefficient value What if Y is dichotomous - Discrete: Ex. Whether or not you renew subscription Linear probability model → subscribe/discrete = B0 + B1 Age + E → predicted probability Logistic Regression Model
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Linear Regression (Linear) vs Logistic (S-Curve, non-linear) Regression Meaning in Bk (if x is continuous) - A unit change in Xk leads to changes in B unit change in log(odds) → exp(B), for 1 unit change in X, the odds of subscrip change by factor of exp(B) exp(B) - 1 → odds change by 100[exp(B) - 1] If x is dummy variable (Xk) - exp(B) = odds ratio between dummy group and reference group Interpretation of Coefficients Sign of Bk - Positive: increase x, then odds increase too - Negative = incr in x leads to decrease in odds - Zero (insignificant) = no significant relationship, changing x won’t change odds Odds - Ratio of (P/1-P), is NOT probability Example: Magazine Subscription - Which segment to target - Age, Income, whether to subscribe or not
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50,000, 3 years, no newborn P = Prob(subscriptions) = exp(B0 + B1 Age + B2 Income) / 1 + exp(B0 + B1 Age + B2 Income)
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- B1 (Age)= .0231 → exp(.0231) = 1.0233 - 1 = 0.023 → if you incr age by 1 unit, the odds of subscription increases by 2.3% (0.023 * 100) - B2 (Income) = .0159 → exp(0.0159)= 1.016 - 1 = .016 → if you increase income by 1 unit, the odds of subscription increase by 1.6% Both p values < 0.05 = significant Measure of Fit - Hit Rate Where model predict correctly on 0 and 1 is Predicted choice → look at Percentage Correct Out of 407 people, model predicts 47% wrong
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If we make constant changes (age), then odds of subscription are constant, not prob of sub (p) Example 2: Customer Acquisition Email and Ad Spend are significant - Email - Ad Spend = 7.5%
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Those who received the email are 4.2x likely to be acquired by company relative to those who did not receive the email $30/0.026 cost per percentage ($1,154) ⇒ $40 for advertising More ad spending brought down the cost (40/.052 = $769) Case Study 1. Most bad loans are in 43-45, and earlier 2. Now, we see most % of bad loans are people < 21 (% represent default rate) 3. P = exp(B0 + B1 G1 + B2 G2 + B3 G3 ) / 1 + exp(B0 + B1 Age + B2 Bad Loan)
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G4 is reference group P = Prob(default) = 4. Are none of them significant because p value > 0.05 1. P-value - 1 = x → 1 unit increase in age, odds of subscription incr by x% (holding everything else constant) 2. Taking exponent , exp(p-value) → increase by a factor of x B1 = 1.123 → exp(1.123) = 3.1, Odds of default for age G1 (22-30 y/o) is 3.1 times higher than default of age G4 (49-60 y/o) expB1) = odds(G1) / odds(G4) B2 = exp(0.909) = 2.5, → odds of default for G2 is 2.5x higher than G4 B3= exp(0.508) = 1.7, → odds of default for G3 is 1.7x higher than G4 Negative example B1 = -2 → exp(-2) = 0.14 FLIP : 1 / exp(-2) → 1/0.14 = 7.4 (take this one), odds of default for G4 is 7.4x higher than odds of default for G1 odds(ref group) / odds(dummy group) Sum / count = % Regression Steps 1. Run with all variables present 2. Take out highest p-values 3. Make correlation matrix in Excel a. Remove highly correlated variables (>.50) 4. Re-run the regression Don’t only rely on hit rate
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- In our example: 94% hit rate, the model performed badly when people did churn - Observed churn rate is 6.4% Exam - Interpret meanings and make predictions if given set of values Quiz 1 R2 cannot decrease as more independent variables are added to the regression equation. Correct! True False Question 2 1 / 1 pts If an examination of the residuals indicates that the assumptions underlying linear regression are not met, the researcher can transform the variables in an attempt to satisfy the assumptions. Correct! True False Question 3 0 / 1 pts
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An Omnibus F test can be used to choose between regression models that are nested within each other (e.g., one model has 4 explanatory variables and the other has a subset of 2 explanatory variables). You Answered True Correct Answer False Partial F test is used between 2 nested models, omnibus F test is used to determine whether or not overall regression is significant (explanatory variables together can explain) Question 4 1 / 1 pts ________ variables may be used as predictors or independent variables by coding them as dummy variables. Interval Correct! Categorical Ratio All of the above Question 5 1 / 1 pts ________ is a state of very high intercorrelations among independent variables. Hypercollinearity Partial collinearity Correct! Multicollinearity Variable collinearity Question 6 1 / 1 pts Out of the three residual plots given below, which of the following violates the assumptions on the error term of a linear regression model? (Note: the plots are between predicted dependent variable and residuals) Look for random scatter plots and no particular shape between predicted y and residuals, so 3 shows that doesnt not satisfy error term
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1 2 Correct! 3 1 and 2 Use the regression output shown below to answer the following questions and use 0.05 as the significance level. The dataset is a sample of 75 cities. height is a variable giving the average height in inches of adult males from the city. tyhpoiddeaths is a variable giving the number of typhoid deaths per 1,000 people in the city. The variables northeast, south and west are all
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dummy variables that are equal to one if the city is in that region and zero otherwise. All cities are located either in the Northeast, the South, the West or the Midwest. linear regression output example.png Question 7 1 / 1 pts Which of the following statement is correct? Midwest is reference group (not included in regression) On average, a male in a Northeast city is 0.73 inches higher than a male in a Midwest city. Correct! On average, a male in a Northeast city is 0.73 inches shorter than a male in a Midwest city. On average, a male in a South city is 0.26 inches shorter than a man in a Midwest city. On average, a male in a West city is 0.26 inches higher than a man in a Midwest city. Question 8 0 / 1 pts Overall, the regions and the number of typhoid deaths can significant explain the variations in adult men's average height. – Yes because p value of typhoid deaths = 0.03 < 0.05 Correct Answer True You Answered False Question 9 0 / 1 pts What is the average male height in a city in the West where the number of typhoid deaths is about 5 per 1,000 people? 1. Write down model Height = B0 + B1 NE + B2 South + B3 West + B4 Deaths + E Intercept (B0) = 68.41 Deaths = 5 * 0.02 (coeff) = NE = 0 South = 0 West = 1 * 0.26 = 0.26 —-------------------------- = 68.41 + 0.10+ .26 = 68.77
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Ex. if it was midwest, all would be 0 68.26 inches Correct Answer 68.78 inches 67.79 inches You Answered 68.52 inches Question 10 1 / 1 pts How much variation in the average male height can be explained by the regions and the number of typhoid deaths? 53% Correct! 56% 75% Logistic Regression Quiz Question 1 Which of the following option is true? Correct! Linear Regression errors values has to be normally distributed but in case of Logistic Regression it is not the case Logistic Regression errors values has to be normally distributed but in case of Linear Regression it is not the case Both Linear Regression and Logistic Regression error values have to be normally distributed Both Linear Regression and Logistic Regression error values have not to be normally distributed Question 2 1 / 1 pts In logistic regression, what do we estimate for each unit change in X? The change in Y multiplied with Y The change in Y from its mean How much Y changes
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Correct! How much the natural logarithm of the odds for Y = 1 changes A marketing research firm was engaged by an automobile manufacturer to conduct a pilot study to examine the feasibility of using logistic regression for ascertaining the likelihood that a family will purchase a new car during the next year. A random sample of 33 suburban families was selected. Data on annual family income (income, in thousand dollars), the current age of the oldest family automobile (age, in years), and whether the family is expecting a new baby were obtained. A follow-up interview conducted 12 months later was used to determine whether the family actually purchased a new car (purchase= 1) or did not purchase a new car (purchase= 0) during the year. A logistic regression model with two predictor variables is assumed to be appropriate. Below is the regression output and use 0.05 as the significance level to answer the following questions. Standard Wald Parameter DF Estimate Error Stats p-value Intercept 1 -4.7393 2.1020 5.0838 0.0242 income 1 0.0677 0.0281 5.8280 0.0158 age 1 0.5986 0.3901 2.3553 0.1249 newborn 1 0.7865 0.2358 11.1253 0.0009 The classification (confusion) matrix is as follows: predicted percentage observed no purchase purchase correct no purchase 13 1 92.9% purchase 5 14 73.7% Overall Percentage 81.8% Outcome = continuous (linear) Outcome = discrete (logistic), ex. Whether or not family bought a car (1 or 0, yes or no) Question 3 1 / 1 pts How much more likely is it that a family expecting a newborn will purchase a new car compared to a family not expecting a new baby? Please type your answer to the nearest whole number.
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Correct! 2 Correct Answers 2 - Newborn p-value is < .05, so → exp(0.7865) = ~2 Always take exp() - 1 → how much change % wise to odds of ___ Question 4 0 / 1 pts An increase of 1 year in the age of the oldest family automobile will increase the odds of purchasing a new car in the next year by 82%, when controlling for family income and whether a new baby is expected. You Answered True Correct Answer False - exp(0.5986) -1 = 0.82 - The variable is not significant , age p-value > 0.05 Question 5 1 / 1 pts How does family income affect the likelihood of new car purchase in the next year, accounting for the age of the oldest family automobile and whether a newborn is expected? An increase of $1,000 in family income leads to a decrease in the odds of new car purchase by 7% Correct! An increase of $1,000 in family income leads to an increase in the odds of new car purchase by 7% Family increase does not have a significant impact on new car purchase An increase of $1,000 in family income leads to an increase in the odds of new car purchase by 0.07% Question 6 1 / 1 pts Which of the following statements are correct? (Choose all that apply) The model is a perfect fit for the data.
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Correct! The model classifies 81.8% of cases correctly overall. The model is less accurate when classifying those who are not going to purchase a new car in the next year. Correct! The model correctly classifies 73.7% of those who are going to purchase a new car in the next year. Question 7 0 / 1 pts What is the estimated probability that a family with annual income of $50 thousand, an oldest car of 3 years and not expecting a new baby will purchase a new car next year? Please type your answer to the nearest whole number (in percentage). You Answered 60.9% Correct Answers 61% - exp(7.7393 + - Insignificant variables can be used in formula - Don’t take exp of beta in the prediction (formula) - Only take exp(beta) for explanations Exam 1 Review - Look over hypothesis testing (3 types) in excel - Will not run excel regressions (just for hypothesis testing) Pivot table, contingency table (observed and expected) Split continuous variable into 2, use T-Test in toolpak 3/12 - Conjoint Analysis Understand how consumers make trade-offs
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- Find optimal combination of features - Contributions of each attribute and each level to overall evaluation of the product/service Rating-based - Use linear regression (OLS), can use output of regression as input for conjoint analysis Choice-based - logistic regression Constant-Sum - Special software Example: Frequent Flyer Service Attribute Attribute Levels Part-worth Range Relative importance Access to clubs Yes or No 1 1 (1 - 0) 1/7 Priority to upgrade Yes or No 2 2 (2 - 0) 2/7 Fee of $50 $0 or $50 -4 4 (0 - -4) 4/7 7 No is the reference groups (part-worth = 0) - Most important is highest number (Fee of $50) and least concern is (Access to clubs), lowest number
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- 8 possible combinations Attributes - Clearly and unambiguously defined and actionable - Attribute levels - Price - Access to clubs - Priority for upgrades - Brand name - The total number of attributes should be kept low Part-worth Utility - Captures the utility value that potential customers attach to certain features Importance Weights $ value for 1 unit of utility ($50/4) What is the $ value for adding access to clubs (50/4) x 1 = $125
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What is $ value for priority to upgrade (50/4) x 2 = $25 Example: Design of Computer Vendor Selection Useful for stages of MR process - Design - Pricing - Positioning - Market share forecasting
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Response format determines the estimation method - Rating → multiple regression - Pairwise Choice → Logistic Regression Conjoint Analysis Tutorial - Relative positive weight, we can make a scatter plot, to find the most important attribute, put people into segments based on preferences (ex. x= Location , y= computer/software) Market Segmentation - Cluster Analysis Needs-Based Segmentation Use descriptor variables to find people to segment Segment Basis - why customers respond differently Segment Descriptors - identify different segments
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Principle Picture Hierarchical vs Partitioning Clustering
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Hierarchical Example Big jump in segments in error in Dendrogram K-Means is more popular K-Means Example
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Profiling 3/21 - Cluster Analysis / PDA Case
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Good for making the product (what consumers want/don’t want) Price: - Segment 1 and 3 are more sensitive to price, they are willing to pay less (red boxes) - Segment 2 and 4 are willing to pay higher (green) for PDA
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Age - Green = higher age Descriptor Analysis (Profiling) settings:
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Select a significance level α and reject the null-hypothesis if the p-value is less than α. Explain, in complete sentences, your findings: Is there a statistically significant association (at α level) between the provided genes? What is the magnitude and the direction of the association?
Select a significance level α and reject the null-hypothesis if the p-value is less than α. Explain, in complete sentences, your findings: Is there a statistically significant association (at α level) between the provided genes? What is the magnitude and the direction of the association?
Submit quiz point(s) possible Construct a 95% confidence interval for H₁₂ with the sample statistics for mean cholesterol content of a hamburger from two fast food chains and confidence interval construction formula below. Assume the populations are approximately normal with unequal variances. Stats =95 mg, s₁ =3.88 mg, n₁ = 19 Confidence interval when variances are not equal (x-2)-1 Ոշ d.f. is the smaller of n₁-1 or n₂-1 Enter the endpoints of the interval. (Round to the nearest integer as needed.) x245 mg. $22.14 mg, n₂ = 12
I conducted an independent t-test for the difference in means between gender and everyday religious decisions. I want to see if there is normality between the samples collected. I conducted a Q-plot which does show normality I would like to know if this is correct?
24) Below is some of the regression output from a simple regression of the number of wins for a major league baseball team and the size amount of money the team is paying its players (expressed in millions of $'s) *fill in blanks of the table* Based on the regression output, what is the correlation between the two variables? *round to 3 decimal places*
Mode = 8 and 11Median = 11Mean= 11.63Range =14Variance = 17.09Standard deviation = 4.1352 Using the standard normal curve, and the data obtained from the histogram (Listed above), please help me answer the following questions:Is a patient that stayed X = 10 days considered as being an extreme or typical length of stay? (show all your data analysis and justify your response in one sentence)What percentage of the patients stayed longer than this?  What percentage of the patients stayed less than this? Please show me how to calculate this properly. b. Is a patient that stayed X = 17 days considered as being an extreme or typical length of stay? (Justify your response in one sentence) What percentage of the patients stayed longer than this?  What percentage of the patients stayed less than this?
Select a significance level α and reject the null-hypothesis if the p-value is less than α. Explain, in complete sentences, your findings: Is there a statistically significant association (at α level) between the provided genes? What is the magnitude and the direction of the association?
use the date form the second picture to answer question 3 please help me with question 3
A child care center wants to determine if there is a relationship between how long a child naps in minutes (20,21,22,23,24,etc.,etc) and incidents of aggression (1,2,3,4,etc.,etc). What type of statistical test should be used?  Group of answer choices Chi Square Independent t-test Dependent t-test ANOVA Correlation Analysis
Please help not graded
HELP PLEASE with finding the test statistic
I am trying to perform a T-Test Two Sample Assuming Equal Variance test in my excel and once I go to data tab, it will not popup the other popup that I need to input and run the test. I have done everything. Can you please help? I have to get this turned in by 11:59 tonight. Thank you.
please answer number 2 correctly in detail like the format of the question correctly please
A physician wants to create a risk profile of childhood obesity. She believes that calories consumed, number of minutes of exercise per week, and number of hours watching TV are important predictors of body mass index. Omultiple regression O binomial test O two-way independent-measures ANOVA Ochi-square test of independence
it y" 10. A dbly līne will be shut down for maintenance if the defect rate exceeds 2.3%. Suppose you adopt a 5% significance level and' take compute the proportion that are defective. For what values of the sample proportion will the assembly line be shut down? a random sample 200 items off the assembly line and 0.06 0.05 0.04 0.02 Back Net
Why would it be better to measure heart rate variance a better outcome measure for autonomic function, than standard deviation from mean heart rate?
When we are running an anova or a t-test, we are comparing the dependent variable across categories of the independent variable. of the probability of error randomness average variance
A bank wants to determine whether a customer's preference for using cash or credit can be used to predict whether they will answer the phone on a weekday evening. What would be the most appropriate procedure to use to analyze data to answer this question? Only choose a test that handles multiple comparisons If such a test is needed. Regression Test of Slope or Correlation O Test for a Difference of Proportions O Test for a Difference of Means O Chi-square test of association O ANOVA (Analysis of Variance)
What is the test statistic?(round to two decimal places) What is the pvalue?(round to three decimal places) Reject or don’t reject null hypothesis?
Estimate can be used to identify two general features for each of the several variance estimates in ANOVA. What are these features?
25
Use a 0.05 significance level to test the claim that the different samples come from populations with the same mean. Use the traditional method.  List                            the null and alternative hypothesis, the critical value, the test statistic, Draw the graph and label the test statistic, critical value and rejection regions. Reject or fail to reject? State the conclusion as outlined in the template or book Your hypothesis test must take up one whole page only (8 1/2" x 11"), typed or written and must be neat. ANOVA Source of Variation SS df MS F P-value Factor 13.500 3 4.500 5.171 0.0011 Error 13.925 16 0.870                 Total 27.425 19
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