Question

Consider the following data on the number of hours taht 7 persons studied for a French test and their scores on the test

Hours studied (x)	3	9	14	4	3	12	10
Test score (y)	20	60	80	30	25	70	60

a) Find the equation of the least squares line that approximates the regression of the test scores on the number of hours studied

b) Predict the average test score of a person who studied 14 hours for the test.

Answer 1

solution:

## R code Hours studied (x) and Test score (y)

x=c(3,9,14,4,3,12,10)
x
y=c(20,60,80,30,25,70,60)
fit=lm(y~x)
summary(fit)

## Answer:

1)
> x=c(3,9,14,4,3,12,10)
> x
[1] 3 9 14 4 3 12 10
> y=c(20,60,80,30,25,70,60)
> fit=lm(y~x)
> summary(fit)

Call:
lm(formula = y ~ x)

Residuals:
1 2 3 4 5 6 7
-3.8140 4.7209 -1.5000 0.9419 1.1860 -1.0116 -0.5233

Coefficients:
Estimate Std. Error t value Pr(>|t|)   
(Intercept) 8.0814 2.3469 3.443 0.0184 *  
x 5.2442 0.2636 19.897 5.93e-06 ***

The equation of the least squares line that approximates the regression
of the test scores on the number of hours studied

2)Average test score of a person who studied 14 hours for the test
i.e x=14

=81.500
thus,
average test score of a person who studied 14 hours for the test is 81.500