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The following table shows the overall GMAT scores of ten randomly selected participants and the number of hours they studied per week:
Score |
Avg. weekly hours |
550 |
12 |
380 |
18 |
430 |
21 |
600 |
20 |
650 |
48 |
680 |
21 |
540 |
14 |
750 |
56 |
710 |
40 |
400 |
10 |
a. Identify the variables.
b. Calculate and interpret the correlation coefficient.
c. Perform a hypothesis test to determine if the population correlation coefficient (ρ) is significantly different from zero [α = 0.10].
d. Estimate the regression equation (calculate bo and b1). Interpret the slope coefficient. Predict the score for a participant who, on an average, studies 20 hours per week.
e. Calculate the coefficient of determination and interpret your results
Solution
a. Identify the variables.
Dependent variable : Score Avg
Independent variable : weekly hours
for remaining questions we will find the solution using excel
we will solve it by using excel and the steps are
Enter the Data into excel
Click on Data tab
Click on Data Analysis
Select Regression
Select input Y Range as Range of dependent variable.
Select Input X Range as Range of independent variable
click on labels if your selecting data with labels
click on ok.
So this is the output of Regression in Excel.
SUMMARY OUTPUT | ||||||||
Regression Statistics | ||||||||
Multiple R | 0.7304 | |||||||
R Square | 0.5334 | |||||||
Adjusted R Square | 0.4751 | |||||||
Standard Error | 95.7770 | |||||||
Observations | 10.0000 | |||||||
ANOVA | ||||||||
df | SS | MS | F | Significance F | ||||
Regression | 1.0000 | 83904.0843 | 83904.0843 | 9.1466 | 0.0165 | |||
Residual | 8.0000 | 73385.9157 | 9173.2395 | |||||
Total | 9.0000 | 157290.0000 | ||||||
Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 99.0% | Upper 99.0% | |
Intercept | 412.8435 | 59.8608 | 6.8967 | 0.0001 | 274.8041 | 550.8829 | 211.9872 | 613.6998 |
weekly hours | 6.0060 | 1.9859 | 3.0243 | 0.0165 | 1.4265 | 10.5855 | -0.6574 | 12.6695 |
b. Calculate and interpret the correlation coefficient.
correlation coefficient r = 0.7304
It can be interpreted as the relationship between Score Avg and Weekly Hours are positively correlated.
c. Perform a hypothesis test to determine if the population correlation coefficient (ρ) is significantly different from zero
d. Estimate the regression equation (calculate bo and b1)
Score Avg = 412.8435+6.0060* weekly hours
Interpret the slope coefficient.
slope coefficient = 6.0060 , As we increase the weekly hours by 1 hours then average score will be increased by 6.0060.
Predict the score for a participant who, on an average, studies 20 hours per week.
Score Avg = 412.8435+6.0060*20
Score Avg = 532.9635
e. Calculate the coefficient of determination and interpret your results
coefficient of determination = 0.5334
It explains 53.34% variation in Score Avg by weekly hours.
Please type answer in word and include how you solved it and work in the word...
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