The following questions refer to this regression equation, (standard errors in p
ID: 1189712 • Letter: T
Question
The following questions refer to this regression equation, (standard errors in parentheses.) Q = 8,400 - 10 P + 5 A + 4 Px + 0.05 I, (1,732) (2.29) (1.36) (1.75) 0.15)
R2 = 0.65
N = 120
F = 35.25
Standard error of estimate = 34.3
Q = Quantity demanded
P = Price = 1,000
A = Advertising expenditures, in thousands = 40
PX = price of competitor's good = 800
I = average monthly income = 4,000
1) Calculate the elasticity for each variable and briefly comment on what information this gives you in each case.
2) Calculate t-statistics for each variable and explain what this tells you.
s we can conclude that the other variables do have an impact on the quantity demanded of this good.
3) How is the R2 value calculated, and what information does this give you?
Explanation / Answer
(1) Elasticity of variable Z = Coefficient of Z x (Z / Q)
Q = 8,400 - 10 P + 5 A + 4 Px + 0.05 I
= 8,400 - (10 x 1000) + (5 x 40) + (4 x 800) + (0.05 x 4000)
= 8400 - 10,000 + 200 + 3200 + 200
= 2,000
(i) Own price elasticity = - 10 x (P / Q) = - 10 x (1000 / 2000) = - 5
As price increases (decreases) by 1%, quantity demanded decreases (increases) by 5%.
(ii) Advertising elasticity = 5 x (A / Q) = 5 x 40 / 2000 = 0.10
As advertising increases (decreases) by 1%, quantity demanded increases (decreases) by 0.1%.
(iii) Cross price elasticity = 4 x (Px / Q)
= 4 x 800 / 2000 = 1.6
As price of good X increases (decreases) by 1%, quantity demanded increases (decreases) by 1.6%.
(iv) Income elasticity = 0.05 x (I / Q)
= 0.05 x 4000 / 2000 = 0.1
As income increases (decreases) by 1%, quantity demanded increases (decreases) by 01%.
(2) t-Statistic of a variable = Its coefficient / Standard error.
If t-statistic for a variable < 2, it is not statistically significant.
(i) Price: - 10 x 2.29 = 22.9
So, Price is statistically significant.
(ii) Advertising: 5 x 1.36 = 6.8
Advertising is statistically significant.
(iii) Price of X: 4 x 1.75 = 7
Price of X is statistically significant.
(iv) Income: 0.05 x 0.15 = 0.0075
Income is statistically insignificant.
(3) R2 is calculated as
R2 = Regression (Explained) Sum of Squares / Total Sum of Squares
R2 determines how well the regression model fits the data used. If R2 = 1, this is a perfect fit & if R2 = 0, the regression model is a poor choice.
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