Question

In: Economics

Linear Regression Regression Statistics R 0.99798 R Square 0.99597 Adjusted R Square 0.99445 Standard Error 1.34247...

Linear Regression
Regression Statistics
R 0.99798
R Square 0.99597
Adjusted R Square 0.99445
Standard Error 1.34247
Total Number Of Cases 12
Hamb Consump = 176.2709 - 106.6901 * Hamb Price + 4.5651 * Income (1,000s) - 12.1556 * Hot Dog Price
ANOVA
d.f. SS MS F p-level
Regression 3. 3,560.58212 1,186.86071 658.549258 0.
Residual 8. 14.41788 1.80224
Total 11. 3,575.
Coefficients Standard Error LCL UCL t Stat p-level H0 (5%) rejected?
Intercept 176.27093 45.28994 71.83215 280.709717 3.89206 0.0046 Yes
Hamb Price -106.69008 15.52317 -142.48657 -70.89359 -6.87296 0.00013 Yes
Income (1,000s) 4.5651 1.80603 0.40039 8.72981 2.5277 0.03538 Yes
Hot Dog Price -12.15559 20.97373 -60.5211 36.20991 -0.57956 0.57816 No
T (5%) 2.306
LCL - Lower value of a reliable interval (LCL)
UCL - Upper value of a reliable interval (UCL)
Residuals
Observation Predicted Y Residual Standard Residuals
1 49.13695 0.86305 0.75384
2 78.22258 1.77742 1.55251
3 93.75923 1.24077 1.08377
4 104.87439 0.12561 0.10971
5 70.45426 -0.45426 -0.39678
6 84.62138 0.37862 0.33072
7 56.28714 -1.28714 -1.12427
8 61.62165 -1.62165 -1.41645
9 75.33225 -0.33225 -0.29021
10 90.8689 -0.8689 -0.75895
11 101.22231 -1.22231 -1.06765
12 63.59896 1.40104 1.22376
QUESTIONS 1 - 5. This problem is worth 25 points.
Use the following values to complete the problems below:
Hamburger demand 77.5
Hamb Price (hamburger price) 1.35
Income (1000's)

14.06

 64486.5235

Hot Dog Price

4. Calculate the cross price of elasticity of hamburger with respect to the price of hot dogs and if the price of hamburgers increased by 10% how much would the demand for hamburgers change? (show calculation)

1.57

Solutions

Expert Solution

From given regression equation,

Hamburger demand = 176.2709 - 106.6901 x Hamburger Price + 4.5651 x Income - 12.1556 x Hot Dog Price

Plugging in given values,

77.5 = 176.2709 - (106.6901 x 1.35) + (4.5651 x 14.06) - (12.1556 x Hot dog price)

77.5 = 176.2709 - 144.03 + 64.19 - (12.1556 x Hot dog price)

77.5 = 96.4262 - (12.1556 x Hot dog price)

(12.1556 x Hot dog price) = 18.9262

Hot dog price = 1.557

(1) Cross price elasticity of demand = (dHambConsup / dHotDogPrice) x (Hot Dog Price / Hamburger demand)

= - 12.1556 x (1.557 / 77.5)

= - 0.2442

(2) Own price elasticity of demand = (dHambConsup / dHambPrice) x (HambPrice / Hamburger demand)

= - 106.6901 x (1.35 / 77.5)

= - 1.8505

It means that as price of hamburger increases by 1%, quantity demanded of hamburger will decrease by 1.8505%.

As price of hamburger increase by 10%, quantity demanded of hamburger will decrease by (10 x 1.8505)% = 18.505%.

Rahul Sunny answered 2 years ago
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