Question

Q4. Professor Video, a college psychology instructor, wants to determine if there is a negative linear correlation between a student's GPA and the number of hours a student spends playing video games per week. She randomly selected twenty students from all her classes and determined their number of hours playing video games per week and their GPA. The sample results were: GPA: 4.00 2.50 3.95 3.90 3.80 2.90 3.10 3.25 1.35 4.00 Hrs Playing:0 15 3 5 0 13 87 12 10 GPA: 1.95 2.75 2.98 2.90 1.50 2.20 3.00 3.15 2.70 2.80 Hrs Playing: 12 13 11 10 1796 813 16 (GPA SUMS: ΣΧ-58.68 ΣΧ2-183.7054) (HRS SUMS: ΣΧ-188 ΣΧ2-2214) a. b. c. d. State the Dependent variable and the Independent variable Label the axes and construct a scatter diagram Compute the sample correlation coefficient, r Calculate the coefficient of determination & explain this result in terms of the dependent and independent variable Write the Regression line equation for the relationship between a student's GPA and the number of hours a student plays video games per week. e. f. Use the Regression equation to predict the GPA of a student who plays 14 hours of video games per week.

Answer 1

Solution: a. State the dependent and theindependentvariable From the given study The dependent variable is GPA The independent variable is Hrs Playing b. Use MINITAB to obtain the scatter plot. MINITAB procedure: Step 1: Choose Graph > Scatterplot. Step 2: Choose Simple, and then click OK Step 3: Under Y variables, enter a column ofYas GPA. Step 4: Under X variables, enter a column ofXas Hrs Playing. Step 5: Click OK

MINITAB output: Scatterplot of GPA vs Hrs playing 4.01 3.5 25 2.0- 1.5- 0- 0 2 468 101 14 1 Hrs playing S- Use MINITAB to obtain the sample correlationcoefficientr MINITAB procedure: Step 1: Choose Stat> Regression> Regression. Step 2: In Response, enter the columncontainingthe response (Y) variable as GPA. Step 3: In Predictors, enter the columns containingthe predictor(X)variables as Hrs Playing. Step 4: Click OK MINITAB output:

Regression Analysis: GPA versus Hrs playing The regression equation is GPA = 4.03-0.116 Hrs playing Predictor Constant Hrs playing 0.11630 0.02614 -4.45 0.000 Coef SE Coef 4.0272 0.2750 14.64 0.000 S 0.552529 R-Sq 52.4% R-Sq (adj) 49.7% . Analysis of Variance Source Regression Residual Error 18 5.4952 0.3053 Total DF MS 1 6.0431 6.0431 19.79 0.000 19 11.5383 Fromthe MINITAB output, the valuef05240.7239 Thus, the value ofthe sample correlationcoefficientris0.7239 Calculate the value ofthe coefficient ofdetemination. From the MINITAB output, the value of coefficient of determination (r) is 52.4%. That is, 0.524.

Interpretation: That is, the coefficient of determination (r.) is 0.524. That is, 52.4% of total observed variation in the GPA points (response varable) that is accourted for by changes in the Hrs playing (explanatory variable) Determine the regression equation for the relationship between a student GPA and number of hours a student plays video games per week. From the MINITAB output, the regression equation is as follows: GPA= 4.0272-0. 1163Hrs Playing Predict the GPA ofa student who plays 14 hours ofvideo games per week. The requiredvalue is, GPA 4.0272-0.1163Hrs Playing 4.0272-0.1163(14) 4.0272-1.6282 2.399 Thus, the predicted value of GPA of a student who plays 14 hours of video games per weekis 2.399