Question

Microeconomic theory states that an inverse relation is likely to exist between price and quantity demanded for normal goods. To examine the validity of this theory in the market of apples, a market researcher observed the daily market price of a box of apples and the quantity of boxes of apples demanded in a local wholesaler fruit market over a period of nine days. By referring to data and additional information displayed below, assist the researcher in performing correlation and simple linear regression analyses on the two variables.

Day	Price in $	Quantity Demanded (in thousands of boxes)
1	13	33.25
2	11.5	34.5
3	9.5	39.2
4	13.5	31.3
5	14.3	32.25
6	15	34.3
7	16	32.35
8	17.5	31.25
9	18.2	27.5

∑?? = 128.5 ∑?? = 295.9 ∑?? 2 = 1896.73 ∑?? 2 = 9808.03 ∑?? ?? = 4164.6

a) State the dependent and independent variables. Briefly explain your selection of the dependent and independent variables.

b) Calculate Sx 2 , Sy 2 and Sxy using the information given above. Display working.

c) Calculate the sample correlation coefficient. Display working

d) Provide an interpretation of the calculated value of the sample correlation coefficient in terms of the relation between price and quantity demanded.

e) Calculate the slope coefficient of the sample linear regression equation. Display working

f) Provide an interpretation of the slope coefficient you calculated in terms of the relation between price and quantity demanded.

g) Calculate the intercept coefficient of the sample linear regression equation. Display working.

h) Provide an interpretation of the intercept coefficient you calculated in terms of the relation between price and quantity demanded

i) State the estimated sample linear regression equation

j) Predict the quantity demanded if price is $19. Display working. Comment on the validity of this prediction.

k) Conduct a test on the slope coefficient to see if a negative relation exists between the two variables. Use a 5% level of significance. Display working of the six steps hypothesis test. The t test-statistic has been calculated. It equals -4.40

l) Calculate the coefficient of determination for the regression line.

m) Provide an interpretation of the calculated coefficient of determination in terms of the relation between price and quantity demanded.

Answer 1