Question

The following table shows the prices of cars in the lineup of a certain automobile manufacturer, along with the profit resulting from the sale of each car:

Sales Price Profit ($44,000, $9,500) ($48,000, $9,600) ($54,000, $12,500) ($56,000, $12,600) ($62,000, $14,000) ($64,000,, $15,000) ($68,000, $17,000)

Mean Sales Price = $56,571 Standard Deviation Sales Price = $8,696 Mean Profit = $12,886 Standard Deviation Profit = $2,743 Correlation = .98

(a) Determine the slope of the least square regression line that predicts the profit from the sales price (round two places after the decimal). _________

(b) Determine the intercept of the least square regression line that predicts the profit from the sales price (round two places after the decimal). _________

(c) Determine the equation of the least square regression line that predicts the profit from the sales price (round two places after the decimal). y ^ = ________

(d) Suppose the manufacturer decides to offer a new car model that will sell for $54,000. Use the regression equation to predict the profit they will make selling this model. $ ________

(e) Calculate the residual for the model that sells for $54,000: $ __________

(f) Fill in the blanks: As the______ increases by ________, we expect the profit to ________ by_________

Answer 1

Here we are going to conduct linear regression. WE want to predict profit for a given value of sales. Since profit is dependent on sales, profit is the response/ dependent variable and sales predictor/ independent.

	X	Y	X^2	Y^2	XY
	44000	9500	1936000000	90250000	418000000
	48000	9600	2304000000	92160000	460800000
	54000	12500	2916000000	156250000	675000000
	56000	12600	3136000000	158760000	705600000
	62000	14000	3844000000	196000000	868000000
	64000	15000	4096000000	225000000	960000000
	68000	17000	4624000000	289000000	1156000000
Total	396000	90200	2.2856E+10	1207420000	5243400000
Mean	56571.43	12885.71
SD	8695.921	2742.522

Mean =

SD =   

The answer may vary a liitle due to rounding off

Regression eq of Y on X

(a) Determine the slope of the least square regression line that predicts the profit from the sales price (round two places after the decimal). _________

Where Slope   'b' =   

Subsituting the values

Slope = 0.3100

(b) Determine the intercept of the least square regression line that predicts the profit from the sales price (round two places after the decimal). _________

Intercept 'a' =

Subsituting the values

intercept = -4652.14

(c) Determine the equation of the least square regression line that predicts the profit from the sales price (round two places after the decimal).

(d) Suppose the manufacturer decides to offer a new car model that will sell for $54,000. Use the regression equation to predict the profit they will make selling this model. $ ________

To find the predicted profit we subsitute the sales value in the reg equation

=-4652.14+0.31x

=-4652.14+0.31 * 54000

= 12088.54

(e) Calculate the residual for the model that sells for $54,000: $ __________

Residual = Actual - predicted

Actual profit for sales 54000 = 12500 .............(from the table)

=12500 - 12088.54

Residual = 411.461

The coeffcient of 'x' in the regression equation is slope. It tells the magnitude and direction of change in 'y' due to unit change in 'x'.

Here slope is positive so the change will be in same direction.

(f) Fill in the blanks: As the sales increases by 1 unit (probably 1000), we expect the profit to increase by 0.31 units.(probably 0.31*1000)