Question

Problem 4 – Analysis of the law of demand 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 Quantity Demanded in $ 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

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

Answer 1

Run a regression analysis in excel followed by below procedures:

1. Go to data tab --> data analysis --> choose Regression

Regression ? Business Business Unrestricted Input OK с Input Y Range: 1 $B$1:$B$10 Cancel Input X Range: $A$1:$A$10 1 Help Constant is Zero 9.5 Labels Confidence Level: 95 96 B Quantity demanded 13 33.25 11.5 34.5 39.2 13.5 31.3 14.3 32.25 15 34.3 16 32.35 17.5 31.25 18.2 27.5 $F$4 A 1 Price 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 1 Output options O Output Range: O New Worksheet Ply: O New Workbook Residuals Residuals Standardized Residuals Residual Plots Line Fit Plots Normal Probability Normal Probability Plots 7

Result:

с D E F G Н - J K L M N O Р Q SUMMARY OUTPUT Quantity demanded 45 40 35 Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations 30 0.86 0.73 0.70 1.74 9 25 y = -0.9703x + 46.732 20 А B 1 Price Quantity demanded 2 13 33.25 3 11.5 34.5 4 9.5 39.2 5 13.5 31.3 6 14.3 32.25 7 15 34.3 8 16 32.35 9 17.5 31.25 10 18.2 27.5 11 12 13 14 15 16 17 18 19 20 21 22 23 15 ANOVA 10 df 5 Significance F 0.003144499 1 0 Regression Residual Total SS MS F 58.40797442 58.407974 19.38846 21.08758114 3.0125116 79.49555556 0 5 10 15 20 7 8 Coe Lower Intercept Price ients 46.732 -0.9703 tandard Error 3.20 0.22 t Stat 14.61 -4.40 P-value 0.00 0.00 Upper Lower .0%Upper 95.0 39.17 54.30 39.17 54.30 -1.49 -0.45 -1.49 -0.45

Linear regression Equation: y = -0.9703x + 46.732

Coefficient of determination (R-squared): 0.73

P-value (Significance F): 0.0003