Question

1) Find the estimated slope. Round answer to three decimal places . 2) If the value of the independent variable is increased by one unit, then find the change in the dependent variable y

Answer 1

First part

We need to find the linear regression line of the given table.

The linear regression line is given by

`\begin{gathered} y=391.179-0.827x \\ \text{where} \\ b_1=-0.827 \\ \text{and} \\ b_0=391.179 \end{gathered}`

The Pearson correlation coefficient is -0.7107. This is a moderate negative correlation, which means there is a tendency for high X variable scores to go with low Y variable scores (and vice versa).

Second part.

Now, If the value of the independent variable is increased by one unit, we have that

`x\longrightarrow x+1`

by substituting this into the linear regression, we get

`y=391.179-0.827(x+1)`

and we have

`\begin{gathered} y=391.179-0.827x-0.827 \\ y=390.352-0.827x \\ \end{gathered}`

then, the change in the dependent variable y is

`\begin{gathered} \\ y=390.352-0.827x \end{gathered}`