# Linear Regression

The data below show the price, in pence per kg, charged by a market-stall holder for apples, and the quantity, in kg, sold in a day when she charges these prices.

Price/p per kg 75 85 100 115 130 150

Quantity sold/kg 50 47 43 40 35 30

Perform linear regression on these, data taking the price as the independent variable and the quantity sold as the dependent variable, and then choose three FALSE statements.

Options.

A. Linear regression gives poor fit to data

B. The regression coefficient is -0.9987 correct to four decimal places.

C. It would not to be wise to extrapolate the quantity of apples she would sell at a price of Â£1.80 per kg from these data

D. The regression equation is y= -0.2646x+69.72 giving the coefficients to four significant figures.

E. The regression equation is y= 69.72x-0.2646 giving the coefficients to four significant figures.

F. The slop of the regression line indicates that for every penny increase in price, she reduces her sales by about 0.26kg a day.

G.The variable x in the regression equation represents the quantity of apples sold in a day

H. The variable x in the regression equation represents the price charged for apples.

Â© BrainMass Inc. brainmass.com December 24, 2021, 4:47 pm ad1c9bdddfhttps://brainmass.com/math/interpolation-extrapolation-and-regression/linear-regression-price-independent-variables-7940

## SOLUTION This solution is **FREE** courtesy of BrainMass!

The calculations are shown in the excel file attached.

The three false statements are:

A. Linear regression gives poor fit to data

The value of r^2 is 0.9973 which indicates that 99.73% of the quantity sold is explained by the price which is good fit

E. The regression equation is y= 69.72x-0.2646 giving the coefficients to four significant figures.

The regression equation is

Y=a+b1 X1= 69.723 + -0.2646 X1

Hence the statement is false

G.The variable x in the regression equation represents the quantity of apples sold in a day

x represents the Price/ per kg. The variable x in the regression equation represents the price charged for apples.

Â© BrainMass Inc. brainmass.com December 24, 2021, 4:47 pm ad1c9bdddf>https://brainmass.com/math/interpolation-extrapolation-and-regression/linear-regression-price-independent-variables-7940