Questions: The following table shows students' test scores on the first two tests in an introductory calculus class. Calculus Test Scores First test, x: 64, 90, 87, 69, 62, 95, 82, 56, 47, 77, 54, 91 Second test, y: 65, 82, 84, 62, 52, 93, 77, 54, 55, 70, 59, 85 Find an equation of the least-squares regression line. Round your answer to three decimal places, if necessary.

The following table shows students' test scores on the first two tests in an introductory calculus class.

Calculus Test Scores

First test, x: 64, 90, 87, 69, 62, 95, 82, 56, 47, 77, 54, 91

Second test, y: 65, 82, 84, 62, 52, 93, 77, 54, 55, 70, 59, 85

Find an equation of the least-squares regression line. Round your answer to three decimal places, if necessary.

Transcript text: The following table shows students' test scores on the first two tests in an introductory calculus class. \begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|c|} \hline \multicolumn{10}{|c|}{ Calculus Test Scores } \\ \hline \begin{tabular}{c} First \\ test, $x$ \end{tabular} & 64 & 90 & 87 & 69 & 62 & 95 & 82 & 56 & 47 & 77 & 54 & 91 \\ \hline \begin{tabular}{c} Second \\ test, $y$ \end{tabular} & 65 & 82 & 84 & 62 & 52 & 93 & 77 & 54 & 55 & 70 & 59 & 85 \\ \hline \end{tabular} Step 1 of 2: Find an equation of the least-squares regression line. Round your answer to three decimal places, if necessary.

Solution

Solution Steps

Step 1: Calculate the means of x and y.

First, sum the values of x and divide by the number of values (n=10) to get x̄ = 73.2. Similarly, sum the values of y and divide by n to get ȳ = 68.9.

Step 2: Calculate the slope (b).

The formula for the slope of the least-squares regression line is:

b = Σ[(xi - x̄)(yi - ȳ)] / Σ(xi - x̄)²