A marketing professor at Givens College is interested in the relationship betwee

Question

A marketing professor at Givens College is interested in the relationship between hours spent studying and total points earned in a course. Data collected on 10 students who took the course last quarter follow. a. Develop an estimated regression equation showing how total points earned is related to hours spent studying. b. Test the significance of the model with alpha = 05. c. Predict the total points earned by Mark Sweeney. He spent 95 hours studying. d. Develop a 95% prediction interval for the total points earn Sweeney.

Explanation / Answer

Here independent variable is hours spent studying and dependent variable is total points earned.

From the information we have to fit regression of dependent variable on independent variable.

We can fit regression in MINITAB.

steps :

ENTER data into MINITAB sheet --> Stat --> Regression --> Regression --> Response : select dependent variable --> Predictors : select independent variable --> Options --> Prediction interval for new observation : 95 --> CLick on prediction limits --> ok --> Results : select second option --> ok --> ok

————— 29-07-2017 09:41:54 ————————————————————

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Regression Analysis: total points earned versus hours spent studying

The regression equation is
total points earned = 5.85 + 0.830 hours spent studying

Predictor Coef SE Coef T P
Constant 5.847 7.972 0.73 0.484
hours sp 0.8295 0.1095 7.58 0.000

S = 7.523 R-Sq = 87.8% R-Sq(adj) = 86.2%

Analysis of Variance

Source DF SS MS F P
Regression 1 3249.7 3249.7 57.42 0.000
Residual Error 8 452.8 56.6
Total 9 3702.5

Predicted Values for New Observations

New Obs Fit SE Fit 95.0% CI 95.0% PI
1 84.65 3.67 ( 76.20, 93.11) ( 65.35, 103.95)   

Values of Predictors for New Observations

New Obs hours sp
1 95.0

Answers :

The regression equation is
total points earned = 5.85 + 0.830 hours spent studying

Significance of the model :

Here we have to test the hypothesis that

H0 : B = 0 Vs H1 : B not = 0

where B is population slope fo hours spent studying.

Assume alpha = level of significance = 0.05

Here test statistic follows F distribution and t-distribution.

Test statistic F = 57.42

P-value = 0.000

Test statistic t = 7.58

P-value = 0.000

Here we see that P-value < alpha

Reject H0 at 5% level of significance.

Conclusion : The population slope for hours spent studying is differ than 0.

95% prediction interval for x = 95 is (65.35, 103.95).

S = standard error of the estimate = 7.523

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