Question

a regression was run to determine if there is a relationship between hours of tv watched per day (x) and number of situps a person can do (y).
the results of the regression were:
y = ax + b
a=-1.332
b = 38.736
r²=0.431649
r=-0.657
use this to predict the number of situps a person who watches 7.5 hours of tv can do (to one decimal place)

Explanation:

Step1: Identify the regression equation

The regression equation is $y = ax + b$ with $a=-1.332$ and $b = 38.736$.

Step2: Substitute the value of x

We want to find y when $x = 7.5$. Substitute $x = 7.5$ into $y=-1.332x + 38.736$.
$y=-1.332\times7.5+38.736$

Step3: Perform the calculations

First, calculate $-1.332\times7.5=-9.99$. Then, $y=-9.99 + 38.736=28.746$.

Step4: Round the result

Rounding $28.746$ to one - decimal place gives $y\approx28.7$.

Answer:

$28.7$