Question

the paired data below consist of the test scores of 6 randomly selected students and the number of hours they studied for the test. by using linear regression, the function ( y = 67.3 + 1.07x ) is obtained, where ( x ) is number of hours studied and ( y ) is score on the test. use the function to predict the score on the test of a student who studies 14 hours. round to the nearest tenth.

hours | score
5 | 64
10 | 86
4 | 69
6 | 86
10 | 59
9 | 87

this question: 1 point(s) possible
submit

a. 82.3
b. 77.3
c. 87.3
d. 88.3

Explanation:

Step1: Identify the linear regression function

The given linear regression function is \( y = 67.3 + 1.07x \), where \( x \) is the number of hours studied and \( y \) is the test score.

Step2: Substitute \( x = 14 \) into the function

We need to find the score for a student who studies 14 hours, so we substitute \( x = 14 \) into the equation:
\[
y = 67.3 + 1.07 \times 14
\]

Step3: Calculate the product

First, calculate \( 1.07 \times 14 \):
\[
1.07 \times 14 = 14.98
\]

Step4: Add to the constant term

Then, add this result to 67.3:
\[
y = 67.3 + 14.98 = 82.28
\]

Step5: Round to the nearest tenth

Rounding 82.28 to the nearest tenth gives 82.3.

Answer:

A. 82.3