Question

suppose ms. carr is interested in the relationship between her students 9th grade math final exam scores and the number of hours they spent studying during the year. she collects information for 15 ninth grade students and uses it to obtain the regression equation, where x is the number of hours spent studying during the year and $hat{y}$ is the predicted final exam score. $hat{y}=1.48x + 75.64$ the scatter plot displays her results. what is the predicted math test score for a student who spends 13 hours studying? $hat{y}=$ (round to 1 decimal place.)

Explanation:

Step1: Substitute \(x = 13\) into the regression equation

We have the regression equation \(\hat{y}=1.48x + 75.64\). Substitute \(x = 13\) into it: \(\hat{y}=1.48\times13+75.64\).

Step2: Calculate the product

First, calculate \(1.48\times13\). Using the formula \(a\times b=(1 + 0.48)\times13=1\times13+0.48\times13=13 + 6.24 = 19.24\).

Step3: Calculate the sum

Then, calculate \(19.24+75.64\). Using the formula \(a + b\), where \(a = 19.24\) and \(b = 75.64\), we get \(19.24+75.64=(19 + 75)+(0.24+0.64)=94+0.88 = 94.88\).

Answer:

\(94.9\)