Chapter 4.6, Problem 11PPS

To determine

The equation of regression line for the data shown below.

Sales Rank	Price ($)
1	43
2	44
3	50
4	61
5	64
6	135
7	108
8	78

Answer to Problem 11PPS

The equation for regression line is $y=9.8x+28.79$ .

Explanation of Solution

Given:The given data is shown as,

Sales Rank	Price ($)
1	43
2	44
3	50
4	61
5	64
6	135
7	108
8	78

Calculation: For the given data the equation for the regression line using the calculatoris written as,

  $y=9.8x+\mathrm{28.79......}\left(1\right)$

To determine

Using the regression line find the estimated price of a pair of 12^th best-selling brand for the given data.

Answer to Problem 11PPS

The estimated price of a pair of 12^th best-selling brand is $146.39.

Explanation of Solution

Given: The given data is shown as,

Sales Rank	Price ($)
1	43
2	44
3	50
4	61
5	64
6	135
7	108
8	78

Calculation: Plugging for $\left(x=12\right)$ in the regression line (1) and simplifying.

  $\begin{array}{c}y=9.8\left(12\right)+\mathrm{28.79......}\left(\text{Plugging for }x=12\right)\\ =146.39\end{array}$

Hence, the price of a pair of 12^th best-selling brand is $146.39.

To determine

Whether the given prediction between the rank and price is reasonable. Explain.

Answer to Problem 11PPS

No, the given prediction is not reasonable.

Explanation of Solution

Given: The given data is shown as,

Sales Rank	Price ($)
1	43
2	44
3	50
4	61
5	64
6	135
7	108
8	78

Calculation:The given prediction between the rank and price for the given data is not a reasonable prediction because it may or may not increase. The price doesn’t increases always as the rank comes in good condition. There are the cases in data set in which rank is good like 1 and still price is $43, whereas in the same data for the lower rank 6 the price is $135. Hence, it does not give the reasonable prediction.