A statistics teacher collected the following data to determine if the number of hours a student studied during the semester could be used to predict the final grade for the course. The Excel output follows the data.
Student | Hours Studying | Final Grade
------- | -------------- | -----------
1 | 42 | 92
2 | 58 | 95
3 | 32 | 81
4 | 39 | 78
5 | 37 | 75
6 | 51 | 88
7 | 49 | 85
8 | 45 | 85
Summary Output:
Regression Statistics
Multiple R 0.752344
R-square 0.566022
Standard error 4.832541
Observations 8
ANOVA Df SS MS F p-value
Regression 1 182.7543 182.7543 7.825578 0.03127
Residual 6 140.1207 23.35345
Total 7 322.875
Coefficient Standard Error t-stat p-value
Intercept 58.00609 9.755659 5.945891 0.001011
Hours 0.608927 0.217674 2.797424 0.03127
a. Determine the least-squares regression line. _______________________
b. Interpret the value of the slope.
c. Determine the standard error of estimate __________________
d. Construct a 95% confidence interval for the average final grade when hours spent studying = 50. Assume that Σ x^2 = 16069 and Σx = 353.
e. Construct a 95% prediction interval for an individual y value when x = 6.5.
f. What percentage of the variation in y is explained by the regression line?
g. In testing the hypotheses H0: β1 = 0 and H1: β1 ≠ 0, what is the value of the calculated test statistic, t?
h. In testing the hypotheses H0: β1 = 0 and H1: β1 ≠ 0, what is the decision rule at the 0.05 significance level?
i. In testing the hypotheses H0: β1 = 0 and H1: β1 ≠ 0, what is the conclusion at the 0.05 significance level? And interpretation?