Question

10. The data set below shows the mileage and selling prices of eight used cars of the same model. Mileage Price 21,000 $16,000 34,000 $11,000 41,000 $13,000 43,000 $14,000 65,000 $10,000 72,000 $12,000 76,000 $7,000 84,000 $7,000 (a) Calculate r , the correlation coefficient between these two variables. r = (b) Interpret the value of r : the association is positive or negative and (strong or moderate or weak or negligible) (c) Compute the regression line for predicting price from mileage. ˆ y = x + (d) Predict the price of a car with 30,000 miles. $ (e) Does the student with 43,000 miles on it have a higher or lower price than the one predicted by the regression line? Higher Lower

Answer 1

Step 1

Plot a graph with the given table.

Step 2

Calculate r, the correlation coefficient between the two variables.

`\begin{gathered} \text{From the graph,} \\ r\text{ = }-0.839 \end{gathered}`

Step 3

Interprete the value of r

`\text{The association is a strong and negative relationship}`

Step 3

Compute the regression line for predicting price from mileage

`\hat{y}=-0.118136x+17688.4`

Step 4

Predict the price of a car with 30,000 miles

`\begin{gathered} \hat{y}=-0.118136(30000)+17688.4 \\ \hat{y}=-3,544.08+17688.4 \\ \hat{y}=\text{\$}14,144.32 \end{gathered}`

Step 5