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 10 students are shown in the table below. Student Verbal Score x Final Grade y 1 55 62 2 37 69 3 50 66 4 66 74 5 56 97 6 31 83 7 32 65 8 78 98 9 46 61 10 29 95 Find the following: (a) The correlation coefficient: r= (b) The least squares line: y^= (c) Calculate the residual for the fourth student

Explanation / Answer

From Excel

a) The correlation coefficient is 0.2179

b) The fitted Regression

y=67.35 + 0.201(Verbal)

c)

The residual for fourt student

y=67.35 + 0.201(66)

y=80.616

SUMMARY OUTPUT Regression Statistics Multiple R 0.217914 R Square 0.047487 Adjusted R Square -0.07158 Standard Error 15.50837 Observations 10 ANOVA df SS MS F Significance F Regression 1 95.92285 95.92285 0.398832 0.545311 Residual 8 1924.077 240.5096 Total 9 2020 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 67.34739 16.05197 4.195584 0.003015 30.33148 104.3633 30.33148 104.3633 verbal 0.201096 0.318426 0.631531 0.545311 -0.5332 0.935388 -0.5332 0.935388

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