# A researcher hypothesizes that undergraduate students who are satis...

## Question

A researcher hypothesizes that undergraduate students who are satisfied with their lives will sleep less than those who are not satisfied. To test this hypothesis, she selects a sample of undergraduate students and asks them to maintain a “sleep log” (Drowsy, 1977), keeping track of the number of hours they sleep during each 24-hour period. These logs are maintained for two weeks. At the end of the two-week period, each participant completes the Satisfaction with Life Scale (Giggle & Smirk, 1969), a reliable, validated measure of general satisfaction with life.

These are the data the researcher obtained:

Participant, Mean Hours of Sleep, SWL Score
01 7.5 23
02 8.3 19
03 9.5 16
04 8.5 20
05 6.0 40
06 8.0 22
07 7.3 30
08 7.0 25
09 8.0 30
10 6.5 36

I. Simple Regression Analysis:
1. What is the criterion variable? Continuous or Categorical for the criterion variable? What is the predictor variable? Continuous or Categorical for the predictor variable?
2. Using SAS to conduct simple regression analysis (attach your syntax and outputs). Based on the outputs, answer Questions 3-11.
3. Write down the regression equation that allows one to predict mean hours of sleep from SWL score.
4. What is “the predicted mean hours of sleep” for someone with an SWL score of 32?
5. What are “the predicted mean hours of sleep” and “the residual” for research participant #7? (Find the values from your SAS outputs and highlight them)
6. What is the value for regression of sums-of-squares (SSreg)? Describe how to compute this value? What is the value for residual sum-of-squares (SSresidual)? Describe how to compute this value?
7. What is the value for the standard error of estimate? Interpret this value in this case?
8. What are the values for coefficients of determination and alienation?
9. We would like to test if the proportion of the variance is significantly accounted for by the predictor. What is the null hypothesis? What is the statistic we use to test this hypothesis? What is your decision (reject or fail to reject) in this case? (Provide statistical evidence to support your decision)
10. We would also like to test if the slope differs significant from 0. What is the null hypothesis? What is the statistic we use to test this hypothesis? What is your decision (reject or fail to reject) in this case? (Provide statistical evidence to support your decision)
11. Regarding outlier diagnosis, which participants are more likely potential outliers? (Provide and describe your statistical evidence; Highlight them in your SAS outputs)

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A researcher hypothesizes that undergraduate students who are satisfied with their lives will sleep less than those who are not satisfied. To test this hypothesis, she selects a sample of undergraduate students and asks them to maintain a “sleep log” (Drowsy, 1977), keeping track of the number of hours they sleep during each 24-hour period. These logs are maintained for two weeks. At the end of the two-week period, each participant completes the Satisfaction with Life Scale (Giggle & Smirk, 1969), a reliable, validated measure of general satisfaction with life.

These are the data the researcher obtained:

Participant, Mean Hours of Sleep, SWL Score
01 7.5 23
02 8.3 19
03 9.5 16
04 8.5 20
05 6.0 40
06 8.0 22
07 7.3 30
08 7.0 25
09 8.0 30
10 6.5 36

I. Simple Regression Analysis:
1. What is the criterion variable? Continuous or Categorical for the criterion variable?
The criterion variable is “Mean Hours of Sleep” and it is Continuous.
What is the predictor variable? Continuous or Categorical for the predictor variable?
The predictor variable is “SWL Score” and it is Continuous.

2. Using SAS to conduct simple regression analysis (attach your syntax and outputs; Based on the outputs, answer Questions 3-11.
SAS Code is given below:
data one;
input Sleep 1-3 SWL_Score 5-6 ;
datalines;
7.5 23
8.3 19
9.5 16
8.5 20
6.0 40
8.0 22
7.3 30
7.0 25
8.0 30
6.5 36
;
run;...

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