Check the solution to "Find the slope of the regression line for..."

Baublysiz

Answered question

2021-12-05

Find the slope of the regression line for the following data.

\begin{array}{cc} x & y \\ 2 & 1 \\ 3 & 3 \\ 4 & 2 \end{array}

We have written the regression line in the form

y = b_{0} + b_{1} x

. So in this problem you only need to find the value of

b_{1}

.
Round your answer to two decimal digits after the decimal point. The answer might be negative. So, your answer could be a number like -2.07, or 0.58, etc.

Answer & Explanation

Feas1981

Beginner2021-12-06Added 16 answers

Step 1

\begin{array}{cc} x & y \\ 2 & 1 \\ 3 & 3 \\ 4 & 2 \end{array}

Step 2
The formula for

b_{1}

is as follows:

b_{1} = \frac{n (\sum x y) - (\sum x) (\sum y)}{n (\sum x^{2}) - {(\sum x)}^{2}}

Calculate the required values are as follows:

\begin{array}{cc} x & y & x y & x^{2} \\ 2 & 1 & 2 & 4 \\ 3 & 3 & 9 & 9 \\ 4 & 2 & 8 & 16 \\ \sum x = 9 & \sum y = 6 & \sum x y = 19 & \sum x^{2} = 29 \end{array}

Step 3
Calculate the value of

b_{1}

is as follows:

b_{1} = \frac{n (\sum x y) - (\sum x) (\sum y)}{n (\sum x^{2}) - {(\sum x)}^{2}}

= \frac{9 (19) - (9) (6)}{3 (29) - {(9)}^{2}}

= \frac{57 - 54}{87 - 81}

= \frac{3}{6}

= 0.5

Therefore, the value of

b_{1}

is 0.5.

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