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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

10 The data set below shows the mileage and selling prices of eight used cars of the same model Mileage Price 21000 16000 34000 11000 41000 13000 43000 14000 65 class=

Respuesta :

Step 1

Plot a graph with the given table.

Step 2

Calculate r, the correlation coefficient between the two variables.

[tex]\begin{gathered} \text{From the graph,} \\ r\text{ = }-0.839 \end{gathered}[/tex]

Step 3

Interprete the value of r

[tex]\text{The association is a strong and negative relationship}[/tex]

Step 3

Compute the regression line for predicting price from mileage

[tex]\hat{y}=-0.118136x+17688.4[/tex]

Step 4

Predict the price of a car with 30,000 miles

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

Step 5

[tex]\begin{gathered} \hat{y}=-0.118136(43000)\text{ + 17688.4} \\ \hat{y}=-5079.848+17688.4 \\ \hat{y}=\text{\$}12608.552\text{ } \\ \hat{y}\approx\text{\$12608.55} \\ \text{The given price for the mileage of 43000 is \$}14000 \\ \text{Therefore, the student with 43000 mileage on it will have a higher price than the one predicted by the regression line.} \end{gathered}[/tex]

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