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Statistics
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Nov 24, 2024
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docx
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Uploaded by erickuria55
1
Research and Analysis
Student’s Name
Institutional Affiliation
Course
Instructor
Due Date
2
Research and Analysis
M9-1
Dependent Variable
Scales Sold
Independent Variable
Months employed
Observations
14+1 =15
Intercept coefficient
113.7453874
Independent variable
coefficient
2.367463621
Regression Model
Scales sold= 113.74 + 2.37 X months employed
R-square
0.790138792
Adjusted R-square
0.773995622
Intercept P-value
0.000108415
Independent variable
P-value
9.39543 x
10
−
6
Your Interpretations
and Analyses
1.
The figure for P. Value of independent variable is less
than 0.05. Therefore, the regression coefficient is
deductively significant
2.
Considering the F. statistic is considerably large, the
model is viewed as having fitted well.
3.
A unit change in the “Months employed” will result in
a change in “scales sold” by 2.37
M9-2
Dependent Variable
Sales
Independent Variable
1
Price
Independent Variable
2
Advertising expenditure
Independent Variable
3
No data provided
Observations
24+1 = 25
Intercept coefficient
275.83333
Coefficient of
Independent variable
1
175
Coefficient of
Independent variable
2
19.68
3
Coefficient of
Independent variable
3
No data is provided
Regression Model
Sales= 275.83 +175 x price + 19.68 x Advertising expenditure
R-square
0.978108766
Adjusted R-square
0.974825081
Intercept P-value
0.023898351
P-value of
Independent variable
1
0.0008316
P-value of
Independent variable
2
1.1263 x
10
−
11
P-value of
Independent variable
3
Data is inexistent
Your Interpretations
and Analyses
1.
The value for p-value of all independent variables is
less than 0.05. as such, the regression coefficient is
perceivably significant.
2.
The f-statistic is sufficiently large. This data suggests
that the model if fitted well.
M9-3
Dependent Variable
Credit card charges
Independent Variable
1
Annual income
Independent Variable
2
Household size
Independent Variable
3
Years of post high-school education
Observations
2,999+1 = 3000
Intercept coefficient
2119.600282
Coefficient of
Independent variable
1
121.3384676
Coefficient of
Independent variable
2
528.0996852
Coefficient of
Independent variable
3
535.3593516
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4
Regression Model
Credit card charges= 2119.60 + 121.34 x annual income +
528.1 x household size + (-535.36) x years of post high-school
education
R-square
0.363202867
Adjusted R-square
0.362565219
Intercept P-value
2.27497 x
10
−
10
P-value of
Independent variable
1
5.4905 x
10
−
262
P-value of
Independent variable
2
4.29401 x
10
−
34
P-value of
Independent variable
3
1.15792 x
10
19
Your Interpretations
and Analyses
1.
The value for p-value of all independent variables is
less than 0.05. as such, the regression coefficient is
perceivably significant.
2.
The f-statistic is sufficiently large. This data suggests
that the model if fitted well.
Related Questions
I have no idea how to fill in the blank in this regression output... please help
arrow_forward
Interpreting Simple Linear Regression
1. Linear correlation coefficient r = 0.794556
2. Coefficient of Determination ( r square) 0.631319
3. Standard Error of the estimate = 12.9668
4. SSR (Explained variation) = 5182.41
5. SSE ( Unexplained variation) = 3026.49
6. Predicted equation or equation of the regression line (Y predicted or hat) = 0.725983X + 16.5523
7. Level of Significance = 0.1
8. Critical Value= 0.378419
Question : Based on the linear correlation coefficient (r) in Line 1, the variables(X,Y) are positively correlated
True
False
arrow_forward
Interpreting Simple Linear Regression
1. Linear correlation coefficient r = 0.794556
2. Coefficient of Determination ( r square) 0.631319
3. Standard Error of the estimate = 12.9668
4. SSR (Explained variation) = 5182.41
5. SSE ( Unexplained variation) = 3026.49
6. SST = 8208.90
7. Predicted equation or equation of the regression line (Y predicted or hat) = 0.725983X + 16.5523
8. Level of Significance = 0.1
9. Critical Value= 0.378419
10. t test = 0.794556
Question
What is meant by a hypothesis? State the hypothesis in this example?
A hypothesis is a claim about the correlation between the Y and X variables in the population under study:
There are two hypothesis (claims)
Null Hypothesis is that (rho) = 0
Alternative Hypothesis is (rho) is not equal to 0
A hypothesis is a claim about the correlation between the Y and X variables in the population under study:
There is only one hypothesis (claim) as follows:
Null Hypothesis is that (rho) = 0
A…
arrow_forward
Interpreting Simple Linear Regression
1. Linear correlation coefficient r = 0.794556
2. Coefficient of Determination ( r square) 0.631319
3. Standard Error of the estimate = 12.9668
4. SSR (Explained variation) = 5182.41
5. SSE ( Unexplained variation) = 3026.49
6. SST = 8208.90
7. Predicted equation or equation of the regression line (Y predicted or hat) = 0.725983X + 16.5523
8. Level of Significance = 0.1
9. Critical Value= 0.378419
Question
What is the meant by the standard error of the estimate? Which number measures the scatter of points about the regression line?
arrow_forward
Interpreting Simple Linear Regression 1. Linear correlation coefficient r = 0.794556 2. Coefficient of Determination ( r square) 0.631319 3. Standard Error of the estimate = 12.9668 4. SSR (Explained variation) = 5182.41 5. SSE ( Unexplained variation) = 3026.49 6. SST = 8208.90 7. Predicted equation or equation of the regression line (Y predicted or hat) = 0.725983X + 16.5523 8. Level of Significance = 0.1 9. Critical Value= 0.378419 10. t test = 0.794556 Question What is meant by a hypothesis? State the hypothesis in this example? A hypothesis is a claim about the correlation between the Y and X variables in the population
arrow_forward
Interpreting Simple Linear Regression
1. Linear correlation coefficient r = 0.794556
2. Coefficient of Determination ( r square) 0.631319
3. Standard Error of the estimate = 12.9668
4. SSR (Explained variation) = 5182.41
5. SSE ( Unexplained variation) = 3026.49
6. SST = 8208.90
7. Predicted equation or equation of the regression line (Y predicted or hat) = 0.725983X + 16.5523
8. Level of Significance = 0.1
9. Critical Value= 0.378419
Question
What is meant by SSR? Which number measures the variation explained by the regression line?
Sum of the Squares Regression (SSR); amount of variation in Y explained by the variation in X explanatory variable
Sum of the Squares Regression (SSR); amount of variation in X explained by the variation in Y
SSR is the percent variation in total variation SST that is explained by the variation in X or SSR/SST = 5182.41/8208.90 = 0.631319 or 63%
Both A and C
arrow_forward
The regression equation is Health Index= y + a Age + ß Blood sugar + 8 Blood Pressure
SE
20986
339.28
Age
Blood sugar
209.2
Blood pressure 207.2
S = 962.233 R-Sq = 86.6% R-Sq (adj) = 76.5%
Coef
Constant
Analysis of Variance
Source
DF
Regression
3
Residual Error. 4
Total
7
SS
Coef
2912
71.95
179.3
225.4
23863180
3703570
27566750
T
7.21
4.72
*
0.92
MS
7954393
925892
F
***
P
0.002
0.009
0.308
**
P
0.032
a) What is dependent and independent variables?
b) Fully write out the regression equation.
c) Fill in the missing values **, ****, and *****.
d) Hence test whether & is significant. Give reasons for your answer.
e) Perform the F Test making sure to state the null and alternative hypothesis.
arrow_forward
Please help me with question d, e, f, g, h, and I. Thank you.
arrow_forward
Drug use The 2011 World Drug Report investigated theprevalence of drug use as a percentage of the populationaged 15 to 64. Data from 22 European countries are
shown in the following scatterplot and regression analy-sis. (Source: World Drug Report, 2011. www.unodc.org/
unodc/en/data-and-analysis/WDR-2011.html)
Dependent variable is CocaineR-squared = 38.1%s = 0.724 with 22 - 2 = 20 degrees of freedomVariable Coefficient SE(Coeff) t-Ratio P-ValueIntercept 0.35707 0.2757 1.295 0.21Cannabis% 0.14264 0.0406 3.512 0.002a) Explain in context what the regression says.b) State the hypothesis about the slope (both numericallyand in words) that describes how use of marijuana isassociated with other drugs.
c) Assuming that the assumptions for inference are satis-fied, perform the hypothesis test and state your conclu-sion in context.
d) Explain what R-squared means in context.e) Do these results indicate that marijuana use leads tothe use of harder drugs? Explain.
arrow_forward
A researcher’s results are shown below using Femlab (labor force participation rate among females) to try to predict Cancer (death rate per 100,000 population due to cancer) in the 50 U.S. states.
Regression Statistics
Multiple R
0.313422848
R Square
0.098233882
Adjusted R Square
0.079447088
Standard Error
32.07003698
Observations
50
Variable
Coefficients
Standard Error
t Stat
Intercept
343.619889
61.0823514
5.62552
Femlab
–2.2833659
0.99855319
–2.28667
Which statement is valid regarding the relationship between Femlab and Cancer?
Multiple Choice
At the .05 level of significance, there isn’t enough evidence to say the two variables are related.
This model explains about 10 percent of the variation in state cancer rates.
If your sister starts working, the cancer rate in your state will decline.
A rise in female labor participation rate will cause the cancer rate to decrease within a state.
arrow_forward
The attached images show linear regression analysis to evaluate the ability of independent variables full and part-time FTEs, number of Medicare certified beds and urban vs. rural setting to predict dependent variable, occupancy rate.
How do you interpret these results, what are the basic assumptions for regression analysis?
arrow_forward
Q1 Data displayed in this graph were standardized. True or false?
Q2 Based on this graph, one can accurately estimate shoe size heritability to be 0.8676. True or false?
arrow_forward
To investigate the relationship between the milage and sales price for a popular car model the pictured scatterplot was used.
a) Based on the excel output that's pictured, what is the estimated regression equation that could be used to predict the price given the miles?
b) Does the model fit the data? (ie whether the regression relationship is statistically significant) Did the estimated regression equation provide a good fit? (ie use the coefficient of determination to explain variability independent variable)
c) Suppose you are considering purchasing a car of this model with 60000 miles. Using the estimated regression equation, predict the price.
arrow_forward
A) Which point from the data has the largest residual?
B) Explain what the residual means in context. Is this point an outlier? An influential point?
The residual means that when the swim time is______, the observed heart rate is about _____ beats less than the predicted rate. When this point is removed, it has an effect on the regression line, so it is influential. The point is not an outlier, because the residual is less than twice the standard deviation.
arrow_forward
mean of x = 2.882, standard deviation = 1.634
Mean of y = 2.588, standard deviation = 0.246
The correlation coefficient is 0.159
slope coefficient for regression line = .0239
y intercept = 2.52
write the regression model
arrow_forward
What variables do Teczar find have the most significant controlled associations with women in national parliaments?
arrow_forward
Please please how to write if based on the following
arrow_forward
There is a dataset of size n = 51 and is for the 50 states and the District of Columbia in the United States. The dependent variable is year 2002 birth rate per 1000 females 18 to 19 years old and independent variable is the violent crime rate (per 1000 population). A simple linear regression model is run with the results given below.
What is the Pearson correlation coefficient between x and y variables?
The R squared of the model?
What kind of relationship there is?
arrow_forward
sample of trucks and their "static weight" and "weight in motion"
weights are in thousands of pounds.
What percent of the variability in static weight can be explained by the linear model rounded to the nearest 10th?
arrow_forward
▼
Set background Clear frame
6.2 2) The program used to create this scatterplot found the line-of-best-fit and reported the
r-squared value as r^2 = 0.805 for the relationship between arm-span and height for
several individuals. What is the correlation coefficient? Is it positive or negative?
Explain how you know.
1850-
1800-
1750-
1700-
00
1650-
1600-
1550-
arm-span (cm)
height (cm)
160.0
R Sq Linear-0805
:
=S
Open c
2 IN
arrow_forward
3. You are working on a regression when accidentally you dump coffee all over yourregression
output.
Using the remaining values, find the missing values in each blank numbered 1-9
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.860644193
R Square
# 4
Adjusted R Square
0.72282625
Standard Error
#5
Observations
32
ANOVA
df
MS
F
Significance F
Regression
2
834.0726419
417.0363209
41.4216016
3.16178E-09
Residual
#2
#1
# 3
Total
31
1126.047188
Coefficients Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
36.90833048
2.190798638
16.84697527 1.62066E-16
32.42764417 41.38901679
cyl
-2.264693597
0.575889243
#7
0.000480375
-3.442519346 -1.086867847
hp
#6
0.01500073 -1.274717745 0.212528465
#8
#9
Screenshot
arrow_forward
Which of the variables is the indepenent variable and dependent variable for the following question.
fit a simple linear regression model to predict latitudes using average monthly range
lat= latitudes
range= the average monthly range between mean montly maximum and minimum temperatures for a selected set of US cities.
arrow_forward
What variables do Teczar find to have the most significant controlled association with women in ministries?
arrow_forward
Only one can be chosen
arrow_forward
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Related Questions
- I have no idea how to fill in the blank in this regression output... please helparrow_forwardInterpreting Simple Linear Regression 1. Linear correlation coefficient r = 0.794556 2. Coefficient of Determination ( r square) 0.631319 3. Standard Error of the estimate = 12.9668 4. SSR (Explained variation) = 5182.41 5. SSE ( Unexplained variation) = 3026.49 6. Predicted equation or equation of the regression line (Y predicted or hat) = 0.725983X + 16.5523 7. Level of Significance = 0.1 8. Critical Value= 0.378419 Question : Based on the linear correlation coefficient (r) in Line 1, the variables(X,Y) are positively correlated True Falsearrow_forwardInterpreting Simple Linear Regression 1. Linear correlation coefficient r = 0.794556 2. Coefficient of Determination ( r square) 0.631319 3. Standard Error of the estimate = 12.9668 4. SSR (Explained variation) = 5182.41 5. SSE ( Unexplained variation) = 3026.49 6. SST = 8208.90 7. Predicted equation or equation of the regression line (Y predicted or hat) = 0.725983X + 16.5523 8. Level of Significance = 0.1 9. Critical Value= 0.378419 10. t test = 0.794556 Question What is meant by a hypothesis? State the hypothesis in this example? A hypothesis is a claim about the correlation between the Y and X variables in the population under study: There are two hypothesis (claims) Null Hypothesis is that (rho) = 0 Alternative Hypothesis is (rho) is not equal to 0 A hypothesis is a claim about the correlation between the Y and X variables in the population under study: There is only one hypothesis (claim) as follows: Null Hypothesis is that (rho) = 0 A…arrow_forward
- Interpreting Simple Linear Regression 1. Linear correlation coefficient r = 0.794556 2. Coefficient of Determination ( r square) 0.631319 3. Standard Error of the estimate = 12.9668 4. SSR (Explained variation) = 5182.41 5. SSE ( Unexplained variation) = 3026.49 6. SST = 8208.90 7. Predicted equation or equation of the regression line (Y predicted or hat) = 0.725983X + 16.5523 8. Level of Significance = 0.1 9. Critical Value= 0.378419 Question What is the meant by the standard error of the estimate? Which number measures the scatter of points about the regression line?arrow_forwardInterpreting Simple Linear Regression 1. Linear correlation coefficient r = 0.794556 2. Coefficient of Determination ( r square) 0.631319 3. Standard Error of the estimate = 12.9668 4. SSR (Explained variation) = 5182.41 5. SSE ( Unexplained variation) = 3026.49 6. SST = 8208.90 7. Predicted equation or equation of the regression line (Y predicted or hat) = 0.725983X + 16.5523 8. Level of Significance = 0.1 9. Critical Value= 0.378419 10. t test = 0.794556 Question What is meant by a hypothesis? State the hypothesis in this example? A hypothesis is a claim about the correlation between the Y and X variables in the populationarrow_forwardInterpreting Simple Linear Regression 1. Linear correlation coefficient r = 0.794556 2. Coefficient of Determination ( r square) 0.631319 3. Standard Error of the estimate = 12.9668 4. SSR (Explained variation) = 5182.41 5. SSE ( Unexplained variation) = 3026.49 6. SST = 8208.90 7. Predicted equation or equation of the regression line (Y predicted or hat) = 0.725983X + 16.5523 8. Level of Significance = 0.1 9. Critical Value= 0.378419 Question What is meant by SSR? Which number measures the variation explained by the regression line? Sum of the Squares Regression (SSR); amount of variation in Y explained by the variation in X explanatory variable Sum of the Squares Regression (SSR); amount of variation in X explained by the variation in Y SSR is the percent variation in total variation SST that is explained by the variation in X or SSR/SST = 5182.41/8208.90 = 0.631319 or 63% Both A and Carrow_forward
- The regression equation is Health Index= y + a Age + ß Blood sugar + 8 Blood Pressure SE 20986 339.28 Age Blood sugar 209.2 Blood pressure 207.2 S = 962.233 R-Sq = 86.6% R-Sq (adj) = 76.5% Coef Constant Analysis of Variance Source DF Regression 3 Residual Error. 4 Total 7 SS Coef 2912 71.95 179.3 225.4 23863180 3703570 27566750 T 7.21 4.72 * 0.92 MS 7954393 925892 F *** P 0.002 0.009 0.308 ** P 0.032 a) What is dependent and independent variables? b) Fully write out the regression equation. c) Fill in the missing values **, ****, and *****. d) Hence test whether & is significant. Give reasons for your answer. e) Perform the F Test making sure to state the null and alternative hypothesis.arrow_forwardPlease help me with question d, e, f, g, h, and I. Thank you.arrow_forwardDrug use The 2011 World Drug Report investigated theprevalence of drug use as a percentage of the populationaged 15 to 64. Data from 22 European countries are shown in the following scatterplot and regression analy-sis. (Source: World Drug Report, 2011. www.unodc.org/ unodc/en/data-and-analysis/WDR-2011.html) Dependent variable is CocaineR-squared = 38.1%s = 0.724 with 22 - 2 = 20 degrees of freedomVariable Coefficient SE(Coeff) t-Ratio P-ValueIntercept 0.35707 0.2757 1.295 0.21Cannabis% 0.14264 0.0406 3.512 0.002a) Explain in context what the regression says.b) State the hypothesis about the slope (both numericallyand in words) that describes how use of marijuana isassociated with other drugs. c) Assuming that the assumptions for inference are satis-fied, perform the hypothesis test and state your conclu-sion in context. d) Explain what R-squared means in context.e) Do these results indicate that marijuana use leads tothe use of harder drugs? Explain.arrow_forward
- A researcher’s results are shown below using Femlab (labor force participation rate among females) to try to predict Cancer (death rate per 100,000 population due to cancer) in the 50 U.S. states. Regression Statistics Multiple R 0.313422848 R Square 0.098233882 Adjusted R Square 0.079447088 Standard Error 32.07003698 Observations 50 Variable Coefficients Standard Error t Stat Intercept 343.619889 61.0823514 5.62552 Femlab –2.2833659 0.99855319 –2.28667 Which statement is valid regarding the relationship between Femlab and Cancer? Multiple Choice At the .05 level of significance, there isn’t enough evidence to say the two variables are related. This model explains about 10 percent of the variation in state cancer rates. If your sister starts working, the cancer rate in your state will decline. A rise in female labor participation rate will cause the cancer rate to decrease within a state.arrow_forwardThe attached images show linear regression analysis to evaluate the ability of independent variables full and part-time FTEs, number of Medicare certified beds and urban vs. rural setting to predict dependent variable, occupancy rate. How do you interpret these results, what are the basic assumptions for regression analysis?arrow_forwardQ1 Data displayed in this graph were standardized. True or false? Q2 Based on this graph, one can accurately estimate shoe size heritability to be 0.8676. True or false?arrow_forward
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