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The owner of a new pizzeria in town wants to study the relationship between weekly revenue and advertising expenditures. All measures are recorded in thousands of dollars. The summary output for the regression model is given below.
ANOVA
dfdf | SSSS | MSMS | FF | Significance FF | |
---|---|---|---|---|---|
Regression | 1 | 19.52147562 | 19.52147562 | 19.03486740 | 0.002403282 |
Residual | 8 | 8.204512367 | 1.02556405 | ||
Total | 9 | 27.72598799 |
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- Data on Advertising Expenditures and Revenue (each measured in thousands of dollars) was collected and Excel was used to run a Regression Analysis on the data. The Excel-generated output is provided below: ANOVA df SS MS F Significance F Regression 1 571.4127907 571.4127907 38.03889695 0.003508906 Residual 4 60.0872093 15.02180233 Total 5 631.5 Coefficients Standard Error t Stat P-value Intercept 32.76744186 2.865238148 11.43620187 0.000333583 Expend 1.578488372 0.255933673 6.167568155 0.003508906 Suppose that you will run the T-test on . a. State the value of , the T Test Statistic (TS) that you would use to run this test. Round off your answer to the fourth decimal place. = Blank 1. Fill in the blank, read surrounding text. b. State the value of the PValue (PV) for the Test Statistic in part (a) above. Round off your answer to the fourth decimal place. The PV = Blank 2. Fill in the blank, read surrounding text.A regression analysis was performed and the summary output is shown below. Regression Statistics Multiple R 0.7802268560.780226856 R Square 0.6087539470.608753947 Adjusted R Square 0.5870180550.587018055 Standard Error 6.7217061336.721706133 Observations 2020 ANOVA dfdf SSSS MSMS F� Significance F� Regression 11 1265.3871265.387 1265.3871265.387 28.006928.0069 4.9549E-054.9549E-05 Residual 1818 813.264813.264 45.18145.181 Total 1919 2078.6512078.651 Step 1 of 2: How many independent variables are included in the regression modelA regression analysis was performed and the summary output is shown below. Regression Statistics Multiple R 0.7802268560.780226856 R Square 0.6087539470.608753947 Adjusted R Square 0.5870180550.587018055 Standard Error 6.7217061336.721706133 Observations 20 ANOVA dfdf SSSS MSMS F� Significance F� Regression 11 1265.3871265.387 1265.3871265.387 28.006928.0069 4.9549E-054.9549E-05 Residual 1818 813.264813.264 45.18145.181 Total 1919 2078.6512078.651 Step 2 of 2: Which measure is appropriate for determining the proportion of variation in the dependent variable explained by the set of independent variable(s) in this model?
- You are analyzing a dataset containing 379 datapoints, and want to use 13 predictor variables to create a multiple variable linear regression model of the data. You conduct an ANOVA analysis, and yield a R² of 38%. Using this information, what would be the F statistic of your analysis?Shown below is a portion of a computer output for regression analysis relating y (dependent variable) and x (independent variable). ANOVA df SS Regression 1 24.061 Residual 10 67.979 Coefficients Standard Error Intercept 11.064 2.049 x −0.566 0.301 (a) What has been the sample size for the above regression analysis? (b) Perform a t-test and determine whether or not x and y are related. Let ? = 0.05. State the null and alternative hypotheses. (Enter != for ≠ as needed.) H0: Ha: Find the value of the test statistic. (Round your answer to three decimal places.) Find the p-value. (Round your answer to four decimal places.) p-value = What is your conclusion? .Based on the ANOVA table given, is there enough evidence at the 0.05 level of significance to conclude that the linear relationship between the independent variables and the dependent variable is statistically significant? Source df SS Regression 2 984.715358 Residual 7 298.884642 Total 9 1283.600000 ANOVA MS F 492.357679 11.531217 42.697806 Significance F 0.006092 Copy Data Ĵ Based on the ANOVA table given, is there enough evidence at the 0.05 level of significance to conclude that the linear relationship between the independent variables and the dependent variable is statistically significant? Source df SS Regression 2 984.715358 Residual 7 298.884642 Total 9 1283.600000 ANOVA MS F Significance F 492.357679 11.531217 0.006092 42.697806 Copy Data
- A car dealership would like to develop a regression model that would predict the number of cars sold per month by a dealership employee based on theemployee's number of years of sales experience. The accompanying regression output was developed based on a random sample of employees. ANOVA df SS Regression 1 79.909407 Residual 23 261.210593 Total 24 341.12 Coefficients Standard Error Intercept 7.271539 1.229763 Slope 0.539854 0.203521 The coefficient of determination is 0.234 Test statistic= 0.704 P-value= 0.014 Construct a 95% confidence interval around the sample slope and interpret its meaning. The confidence interval is (__________,_________). (Type an integer or decimal rounded to three decimal places as needed.)Dex Research Limited conducted a research to investigate consumer characteristics that can be used to predict the amount charged by credit card users. The following multiple regression output is based on a data collected by this research company on annual income, household size and annual credit card charges for a sample if 50 consumers. Regression Statistics Multiple R 0.9086 R Square A Adjusted R Square 0.8181 Standard Error 398.091 Observations B ANOVA df SS MS F Significance F Regression 2 D E G 1.51E-18 Residual C 7448393 F Total 49 42699149 Coefficients Standard Error t Stat P-value Intercept 1304.9048 197.6548 6.6019 3.29E-08 Income ($1000s) 33.133 3.9679 H 7.68E-11 Household Size 356.2959 33.2009 10.7315 3.12E-14 a. Complete the missing entries from A to H in this output b. Estimate the annual credit card charges for a three-person household with an annual income of $40,000.c. Did the estimated regression…A researcher is interested in examining the relationship between spousal abuse and child abuse. Specifically, they are interested in determining whether there is a predictive relationship between spousal abuse and child abuse in 5 county social services offices. Calculate the linear regression line for the following data. Note you have already calculated the first step to this analysis (Pearson's Correlation)
- Let's study the relationship between brand, camera resolution, and internal storage capacity on the price of smartphones. Use α = .05 to perform a regression analysis of the Smartphones01CS dataset, and then answer the following questions. When you copy and paste output from MegaStat to answer a question, remember to choose to "Keep Formatting" to paste the text. a. Did you find any evidence of multicollinearity and variance inflation among the predictors. Explain your answer using a VIF analysis. b. Copy and paste the normal probability plot for your analysis. Is there any evidence that the errors are not normally distributed? Explain. c. Copy and paste the Residuals vs. Predicted Y-values. Does the pattern support the null hypothesis of constant variance for the errors? Explain. d. Study the residuals analysis. Which observations, if any, have unusual residuals? e. Study the residuals analysis. Calculate the leverage statistic. Which observations, if any, are high leverage…A multiple regression analysis produced the following tables. Summary Output Regression Statistics Multiple R 0.978724022 R Square 0.957900711 Adjusted R Square 0.952287472 Standard Error 67.67055418 Observations 18 ANOVA df SS MS F Significance F Regression 2 1562918.941 781459.5 170.6503 4.80907E-11 Residual 15 68689.55855 4579.304 Total 17 1631608.5 Coefficients Standard Error t Stat P-value Intercept 1959.709718 306.4905312 6.39403 1.21E-05 X1 -0.469657287 0.264557168 -1.77526 0.096144 X2 -2.163344882 0.278361425 -7.77171 1.23E-06 Using α = 0.01 to test the…Police sometimes use footprint evidence to estimate the height of a suspect. Data was collected from 36 randomly selected men in Nebraska in 2001. The regression model assumptions have been checked, and they are all satisfied. We want to test if there is a positive linear association between shoe print size and average height. The p-value of the appropriate test was found to be 0.0006. (a) Give your brief conclusion. Note that no significance level is provided. (b) Give your conclusion in the context of the problem. (This question will be marked manually by your instructor).