Question
Multivariate Linear Demand Curve: Lorena Bob wishes to analyze demand for Cleavers , a new cutting device, dubbed product x, by estimating Qdx = a
Multivariate Linear Demand Curve:
Lorena Bob wishes to analyze demand for Cleavers, a new cutting device, dubbed product x, by estimating
Qdx = a - b Px + c Py + d I + e AD
She creates a worksheet in EXCEL with 5 columns: Qdx, Px, Py, I, AD. Here Qdx is the demand for x, Px is the price of x, Py is the average price in dollars of another product Y, and I is dollars of household income and AD is total advertising expenditure for x.
In a typical market, the Px is $ 100, Py is $ 50, average family income is $ 40,000, and AD equals $ 1,000.A portion of the Excel output is reproduced below.
SUMMARY OUTPUT
Regression Statistics
Multiple R0.97757806
R Square0.9400000
Adjusted R Square0.930000
Standard Error40
Observations25
ANOVA
DSSMSFSignific F
Regression21.5932770.796638226.30046.19E-15
Residual230.07392570.00352
Total251.6672026
CoefficientsSTD Error
Intercept20001596.0
X Variable 1-0.255
X Variable 2104
X Variable 31.50.022
X Variable 4100.5
1.Write down the equation that was estimated in EXCEL.
Qdx = 2,000 - .25Px + 10PY + 1.5I + 10AD
2.Evaluate the slope with respect to each independent variable.Provide an interpretation for these values.Perform an impact-analysis.
dQdx / dPx = -.25 unit increase in Px, Qdx falls by .25
dQdx / dPy = 10 unit increase in Py, Qdx rises by 10
dQdx / dI = 1.5 unit increase in I, Qdx rises by 1.5
dQdx / dAD = 10 unit increase in AD, Qdx rises by 10
3.Given the initial values, predict the level of sales in this market.Derive a 95% confidence interval around this prediction.
Level of sales in this market = 2,000 - .25 x 100 + 10 x 50 + 1.5 x 40,000 + 10 x 1,000
= 2,000 - 25 + 500 + 60,000 + 10,000
= 72,475
4.Use the initial values to calculate and interpret the following entities:
a.own price elasticity of demand for x: =(-.25 X 100) / 72,745
increase in Px, Qdx falls by = -.00034
b.cross price elasticity of demand between x and y: = (10 x 50) / 72,745
increase in Py, Qdx rise by = .0069
c.income elasticity of demand for x:= (1.5 x 40,000) / 72,745
increase in I, Qdx rises by = .83
5.Is Px a significant variable in this model -- test at 95%.
The calculated t value =
The table value of t = 1.725
Can you reject the null hypothesis (of no significance) ? _______
6.Is Py a significant variable in this model -- test at 95%.
The calculated t value =
The table value of t = 1.725
Can you reject the null hypothesis (of no significance) ? _______
7.Test at 99% whether x is a normal good
The calculated t value =
The table value of t = 1.725
Can you reject the null hypothesis (of "not a normal good") ? _______
Provide a precise interpretation of R squared for this problem
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