A study was conducted to determine whether the final grade of a student in an in

Question

A study was conducted to determine whether the final grade of a student in an introductory psychology course is linearly related to his or her performance on the verbal ability test administered before college entrance. The verbal scores and final grades for 1010 students are shown in the table below.

Find the following:

(a) The correlation coefficient: r= ___?___

(b) The least squares line: y = ___?___

(c) Calculate the residual for the first student: ___?___

Student Verbal Score x Final Grade y 1 75 84 2 58 71 3 73 64 4 42 93 5 52 67 6 59 74 7 35 64 8 61 81 9 50 93 10 31 85

Explanation / Answer

a) Correlation Coefficient r = -0.19079

b) y = 85.36268-0.14483x

c) For first studeny who verbal score is 75

Predicted final grade = 85.36268-0.14483*75 = 74.50072

Residual = 84-74.50072 = 9.49928

SUMMARY OUTPUT Regression Statistics Multiple R 0.190789 R Square 0.0364 Adjusted R Square -0.08405 Standard Error 11.61689 Observations 10 ANOVA df SS MS F Significance F Regression 1 40.78305 40.78305 0.302204 0.597512 Residual 8 1079.617 134.9521 Total 9 1120.4 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 85.36268 14.59091 5.850403 0.000383 51.71599 119.0094 51.71599 119.0094 X Variable 1 -0.14483 0.263449 -0.54973 0.597512 -0.75234 0.462689 -0.75234 0.462689

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