Please Answer each question item (a through i) in the space provided below. A st
ID: 3295077 • Letter: P
Question
Please Answer each question item (a through i) in the space provided below.
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 .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 x 2 = 16069 and x = 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: 1 = 0 and H1 : 1 0 what is the value of the calculated test statistic, t ?
h. In testing the hypotheses H0: 1 = 0 and H1 : 1 0 what is the decision rule at the 0.05 significance level?
i. In testing the hypotheses, H0: 1 = 0 and H1 : 1 0 what is the conclusion at the 0.05 significance level? And interpretation?
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
Explanation / Answer
a. Determine the least-squares regression line. _______________________
y = 58.00609 + 0.608927 * hours
b. Interpret the value of the slope.
for every increase in 1 hour change in y is 0.608927
c. Determine the standard error of estimate ________________
s = 4.832541
d. Construct a 95% confidence interval for the average final grade when hours spent studying = 50
Assume that x 2 = 16069 and x = 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?
R^2 = 0.566022
g. In testing the hypotheses H0: 1 = 0 and H1 : 1 0 what is the value of the calculated test statistic, t ?
t =2.797424
h. In testing the hypotheses H0: 1 = 0 and H1 : 1 0 what is the decision rule at the 0.05 significance level?
if p-value < 0.05
we reject the null
i. In testing the hypotheses, H0: 1 = 0 and H1 : 1 0 what is the conclusion at the 0.05 significance level? And interpretation?
p-value = 0.03127 < 0.05
hence we reject the null and conclude that there is significant evidence that there is relation with these tow variables