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 vertical ability test administered before college entrance. The verbal scores and final grades for 10 students are shown in the table below

(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 59 93 75 65 75 4 38 76 75 80 37 37 48 43 27 7 9 10 94 70 Find the following (a) The correlation coefficient r = (b) The least squares line: y= (c) Calculate the residual for the third student

Explanation / Answer

Solution1a:

r=0.305

Explanation is

Rcode is

x <- c(59,75,33,38,42,37,37,48,43,27)
y <- c(93,75,65,76,75,80,84,77,94,70)
cor(x,y)

outoput:0.3050106

SOlution1b:

the regression eq is

y=70.027+0.202x

slope=0.202

y intrercept=70.027

Rcode is:

x <- c(59,75,33,38,42,37,37,48,43,27)
y <- c(93,75,65,76,75,80,84,77,94,70)

regmod <- lm(y~x)  
summary(regmod)

output:

Call:

lm(formula = y ~ x)

Residuals:

Min 1Q Median 3Q Max

-11.697 -4.992 -2.218 5.495 15.282

Coefficients:

Estimate Std. Error t value Pr(>|t|)   

(Intercept) 70.0267 10.2306 6.845 0.000132 ***

x 0.2021 0.2231 0.906 0.391473   

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Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 9.337 on 8 degrees of freedom

Multiple R-squared: 0.09303, Adjusted R-squared: -0.02034

F-statistic: 0.8206 on 1 and 8 DF, p-value: 0.3915

SOlution1c:

residual =observed -predicted

y hat for x=33

is

y=70.027+0.202(33)

y= 76.693

residual=observed -predicted

=65-76.693

=-11.693

ANSWER:-11.693

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