Question

the following table gives the data for the hours students spent on homework and their grades on the first test. the equation of the regression line for this data is $hat{y}=61.052 + 0.521x$. this equation is appropriate for making predictions at the 0.05 level of significance. if a student spent 35 hours on their homework, make a prediction for their grade on the first test. round your prediction to the nearest whole number.

hours spent on homework and test grades

hours spent on homework	34	12	43	37	12	29	49	52	8	30
grade on test	75	68	77	94	61	86	90	80	64	75

Explanation:

Step1: Identify the regression equation and x - value

The regression equation is $\hat{y}=61.052 + 0.521x$, and $x = 35$ (hours spent on homework).

Step2: Substitute x into the equation

$\hat{y}=61.052+0.521\times35$.
First, calculate $0.521\times35 = 18.235$.
Then, $\hat{y}=61.052 + 18.235=79.287$.

Step3: Round the result

Rounding $79.287$ to the nearest whole number gives $79$.

Answer:

79