Question

Age and the Price of Wine. For a particular red wine, the following data show the auction price for a 750-milliliter bottle and the age of the wine in June of 2016 (WineX website).

Age (years) 36 20 29 33 41 27 30 45 34 22

Price ($) 256 142 212 255 331 173 209 297 237 182

a. Develop a scatter diagram for these data with age as the independent variable.

b. What does the scatter diagram developed in part (a) indicate about the relationship between age and price?
c. Develop the least squares estimated regression equation.

d. Provide an interpretation for the slope of the estimated equation.

Answer 1

a.

b. As we see that there is increasing trend which means for every increase in x there is corresponding increase in y.

So there is positive correlation and as data are not much scattered there is stron positive correlation between x and y.

c.

Sum of X = 317
Sum of Y = 2294
Mean X = 31.7
Mean Y = 229.4
Sum of squares (SSX) = 552.1
Sum of products (SP) = 3838.2

Regression Equation = ŷ = bX + a

b = SP/SSX = 3838.2/552.1 = 6.952

a = MY - bMX = 229.4 - (6.95*31.7) = 9.022

ŷ = 6.952X + 9.022

d. With every increase in x, there is 6.952 increase in y and this value is slope.