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Researchers record the age and life satisfaction score (rated from 1 to 10, with higher scores...

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Basic Math

  1. Researchers record the age and life satisfaction score (ratedfrom 1 to 10, with higher scores indicating greater lifesatisfaction) among a sample of college students. They hypothesizethat age will predict life satisfaction among college students.Compute an analysis of regression.

X (Age in Years)

Y (Life Satisfaction)

18

6

18

8

26

7

28

5

32

9

19

8

21

5

20

6

25

7

42

9

F-statistic                            ______

Decision                              ______

  1. Suppose that a computer glitch inflated each life satisfactionscore by two. Subtract 2 points from each life satisfaction scoreto correct this. Compute an analysis of regression.

F-statistic                            ______

Decision                              ______

  1. Instead, suppose that the computer glitch divided each lifesatisfaction score by half. Multiply each life satisfaction scoreby 2 to correct this. Compute an analysis of regression.

F-statistic                            ______

Decision                              ______

  1. Does the F-statistic or the decision change fromQuestion 1 to 3? Explain why.

Answer & Explanation Solved by verified expert
3.5 Ratings (315 Votes)

The regression output is:

r² 0.230
r   0.479
Std. Error   1.388
n   10
k   1
Dep. Var. Y (Life Satisfaction)
ANOVA table
Source SS   df   MS F p-value
Regression 4.5917 1   4.5917 2.38 .1612
Residual 15.4083 8   1.9260
Total 20.0000 9  
Regression output confidence interval
variables coefficients std. error    t (df=8) p-value 95% lower 95% upper
Intercept 4.6667
X (Age in Years) 0.0937 0.0607 1.544 .1612 -0.0462 0.2337

F-statistic = 2.38

Decision:

Since the p-value (0.1612) is greater than the significance level (0.05), we cannot reject the null hypothesis.

The regression output is:

r² 0.230
r   0.479
Std. Error   1.388
n   10
k   1
Dep. Var. Y (Life Satisfaction)
ANOVA table
Source SS   df   MS F p-value
Regression 4.5917 1   4.5917 2.38 .1612
Residual 15.4083 8   1.9260
Total 20.0000 9  
Regression output confidence interval
variables coefficients std. error    t (df=8) p-value 95% lower 95% upper
Intercept 2.6667
X (Age in Years) 0.0937 0.0607 1.544 .1612 -0.0462 0.2337

F-statistic = 2.38

Decision:

Since the p-value (0.1612) is greater than the significance level (0.05), we cannot reject the null hypothesis.

No, the decision did not change.
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