Question

A vehicle manufacturing company wants to investigate how the price of one of its car models depreciates with age. The research department at the company took a sample of nine cars of this model and collected the following information on the ages (in years) and prices (in thousands of RM) of these cars.

Age 6 4 3 10 2 5 8 7 9 Price 39 93 99 19 148 47 18 37 20

(a) Construct a scatter diagram for these data. Does the scatter diagram exhibit a linear relationship between ages and prices of cars? (b) Find the regression line with price as a dependent variable and age as an independent variable. (c) Give a brief interpretation of the values of a and b calculated in part (b). (d) Predict the price of a 7-year-old car of this model. (e) Construct a 95% confidence interval for B. (f) Test at 5% significance level whether B is negative.

Answer 1

a) We need to take age (x) on the horizontal axis and Price(y) on the vertical axis. Then plotting the different combinations of (x,y) on the graph we will find a negative linear relationship between x and y. That is, as X increases y decreases and vice versa.

b) Regression line is given as:

y = a + bx

Where, b= Sxy/Sxx and a= ybar - b*xbar

Sxy= /n

Sxx = /n

Y bar = /n

X bar = /n

So from the data we get, b= -15.217 and a= 149.078

So the regression line is given as,

y= 149.078 -15.217x

c) b is the slope of the regression line. With a value of -15.217 it tells us that for every 1 unit increase in x, y decreases by 15.217

a is the y intercept with a value of 149.078, ie when x=0, y will be ~150

d) When x=7, putting it in the regression equation, we get y=43