Question

(1 point) 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 38 77 2 39 90 3 60 71 4 67 73 5 42 69 6 77 84 7 38 77 8 69 74 9 33 63 10 35 65 Find the following: (a) The correlation coefficient: r= (b) The least-squares line: ŷ = (c) Calculate the residual for the seventh student:

Answer 1

For the given data using Regression in Excel we get output as

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.275258421
R Square	0.075767199
Adjusted R Square	-0.039761902
Standard Error	8.395493078
Observations	10
ANOVA
	df	SS	MS	F	Significance F
Regression	1	46.22556781	46.22557	0.655828	0.441457184
Residual	8	563.8744322	70.4843
Total	9	610.1
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	67.48118105	8.828676677	7.643408	6.05E-05	47.12221614	87.84014596
x	0.136924075	0.169077142	0.809832	0.441457	-0.252968512	0.526816663
RESIDUAL OUTPUT
Observation	Predicted y	Residuals
1	72.68429591	4.315704088
2	72.82121999	17.17878001
3	75.69662557	-4.696625568
4	76.65509409	-3.655094095
5	73.23199221	-4.231992213
6	78.02433485	5.975665152
7	72.68429591	4.315704088
8	76.92894225	-2.928942245
9	71.99967554	-8.999675535
10	72.27352369	-7.273523686

So from the above output

( a )  The correlation coefficient: r = 0.2753

( b )  The least-squares line:

ŷ = 67.4812 + 0.1369  x

( c )

the residual for the seventh student is = 4.3157

Note : I rounded all values to four decimals .So round the decimals according to your answers from the output