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.

Find the following:

(a) The correlation coefficient: r=

(b) The least squares line: y^=

(c) Calculate the residual for the third student:

Student Verbal Score x Final Grade y 1 33 99 2 74 69 3 61 96 4 68 91 5 47 82 6 64 75 7 32 69 8 38 61 9 30 95 10 72 79

Explanation / Answer

Go to excel Data->Data analysis -> regression.

Following is the output of regression analysis:

(A)

The correlation coefficient is:

r = 0.1022

(B)

The least square line is

y' = 85.549 - 0.076x

(c)

The predicted value of X = 61 is

y' = 85.549 - 0.076*61 =  80.913

The residual for third student is

Residual = Observed - Predicted = 96 - 80.913 = 15.087

SUMMARY OUTPUT Regression Statistics Multiple R 0.10215939 R Square 0.010436541 Adjusted R Square -0.113258891 Standard Error 13.93740675 Observations 10 ANOVA df SS MS F Significance F Regression 1 16.38954396 16.38954396 0.084372889 0.778844058 Residual 8 1554.010456 194.251307 Total 9 1570.4 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 85.54901268 14.29181034 5.985876571 0.000328528 52.59203896 118.5059864 Verbal Score x -0.076088876 0.261950789 -0.290470117 0.778844058 -0.680148478 0.527970725

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