Question

Jane wishes to investigate the association between the average length of sleep in hours and an NUS student’s Cumulative Average Point (CAP). She collated responses from 250 undergraduates, found the correlation to be 0.87, and established a linear regression equation of CAP (y) against the length of sleep (x):

y=0.5x+0.5

Which of the following is true?

A) If we group the data into different faculties and we take the average C.A.P and average length of sleep per faculty, we will be able to get the same linear regression equation with the same correlation coefficient, r.

B) An increase in the length of sleep by 1 hour is expected to increase CAP by 0.87.

C) Changing the units for length of sleep from hours to minutes does not change the linear regression equation.

D) If we plot a new scatter diagram with x = CAP and y = numbers of hours of sleep, r value will not change.

Answer 1

Sol:

Ex we build a linear regressio of y on x(avergaes are 3 and 4 isy^=   0.5714286 +1.2857143 * x

Take new data points x1 <- c(5,2,1)
y1 <- c(4,6,2)

with same avergae

y^= 3.3846154 +0.2307692 *x

Statement A is false

slope=0.5

An increase in the length of sleep by 1 hour is expected to increase CAP by 0.50

Statement B is false

for statement C

x <- c(100,300,400)
y <- c(2,4,6)
df=data.frame(x,y)
linmod <- lm(y~x,data=df)
coefficients(linmod)

y^= 0.57142857+ 0.01285714 *x

coeffcients will change linear regression equation

statement (3) is false

r=correaltion coeffiecient between x and y

it will not change if we change y to x and x to y

statement 4 is true

D) If we plot a new scatter diagram with x = CAP and y = numbers of hours of sleep, r value will not change.

C) Changing the units for length of sleep from hours to minutes does not change the linear regression equation.