Question

46 2 (6 points) 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 all 10 students in the class are shown in the table below. Student Verbal Score x Final Grade y 1 86 42 77 3 41 87 4 39 98 5 79 75 6 41 90 7 62 8 69 66 9 32 64 10 54 68 49 Find the following: (a) The correlation coefficient: r = (b) The least squares line: û = (c) Calculate the residual for the tenth student:

Answer 1

Solution-1:

use corr function to get the correlation coefficient.

lm function to fit a linear model of y on x

coefficient function to get slope and y intercept

Rcode:

verbalscore_x <- c(46,42,41,39,79,41,49,69,32,54)
Final_grade_y <- c(86,77,87,98,75,90,62,66,64,68)
cor(verbalscore_x,Final_grade_y)
lmod <- lm(Final_grade_y~verbalscore_x)
coefficients(lmod)

output:

Final_grade_y <- c(86,77,87,98,75,90,62,66,64,68)
> cor(verbalscore_x,Final_grade_y)
[1] -0.3234456
> lmod <- lm(Final_grade_y~verbalscore_x)
> coefficients(lmod)
(Intercept) verbalscore_x
90.9131396 -0.2766898

ANSWER(A)

r= -0.3234456

y^= 90.9131396 -0.2766898 *x

for tenth student,x=54,y^=90.9131396-0.2766898 *54= 75.97189

Residual=observed y-predicted y

=68-75.97189

Residual=-7.97189

Solution-2:

Rcode:

Females <- c(2,1,4,1,3,3,3,4,0,1)
males <- c(6,8,6,6,7,6,6,7,9,5)
t.test(Females,males,var.equal = TRUE,conf.level = 0.977)

output:

data: Females and males
t = -7.621, df = 18, p-value = 4.857e-07
alternative hypothesis: true difference in means is not equal to 0
97.7 percent confidence interval:
-5.834883 -2.965117
sample estimates:
mean of x mean of y
2.2 6.6

ANSWER:

confidence interval = (-5.834883 ,-2.965117)