What is the correlation coefficient for this model? 0.94 0.97 -0.88 0.88 Which o

Question

What is the correlation coefficient for this model?

0.94

0.97

-0.88

0.88

Which of these statements below is true?

88% of the variability of the test grades is explained by the number of hours studied

94% of the variability of the hours studied is explained by the test grade

88% of the variability of both variables is explained by the regression

Both B and C are true

What is the sum of squares error for the model?

3.031

33.35

204.22

18.565

Based on this regression model, if a student spends an average of 11 hours per week studying, what will his/her expected test grade be (round to the nearest integer)?

95

83

90

Not enough information to answer this question

What is the dependent variable (study hours per week or test grade)?

Study hours per week is the dependent variable

Test grade is the dependent variable

Both variables are dependent on each other

Neither of the variables are dependent

Study hrswk Test Grade 67 94 93 92 91 65 85 95 84 15 17 16 14 12 13 20 65

Explanation / Answer

Here the regression output for the the given problem

(a) Here correlation coefficient = 0.9360 or 0.94 (option A is correct)

(b) Here R2 = 0.88 so option A is correct. 88% of the variability of the test grades is explained by the number of hours studied

(c) Sum of squares error = 204.2156

(d) Here the regression line equation

y^ = 59.18 + 2.146x

y^ = 59.18 + 2.146 * 11 = 83 (option b is correct)

(e) Here dependent variable is Test grade , as it is dependent on the study hours per week.

SUMMARY OUTPUT Regression Statistics Multiple R 0.936022113 R Square 0.876137397 Adjusted R Square 0.862374885 Standard Error 4.763468066 Observations 11 ANOVA df SS MS F Regression 1 1444.51162 1444.51162 63.66116 Residual 9 204.215652 22.690628 Total 10 1648.72727 Coefficients Standard Error t Stat P-value Intercept 59.1826087 3.48818552 16.9665886 3.85E-08 study hrs/wk 2.146086957 0.26897385 7.97879417 2.26E-05

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