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 Qd_x is the demand for x, P_x is the price of x, P_y 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.

Qd_x = 2,000 - .25P_x + 10P_Y + 1.5I + 10AD

2.Evaluate the slope with respect to each independent variable.Provide an interpretation for these values.Perform an impact-analysis.

dQd_x / dP_x = -.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