Deck & Blacker is a maker of small kitchen appliances. Its economists estimated
ID: 1095098 • Letter: D
Question
Deck & Blacker is a maker of small kitchen appliances. Its economists estimated the following demand for toaster oven using data gathered over 16 quarters from 10 major retail distributors of its product. This type of sample which involves the use of cross-sectional and time series data is referred to as a pooled sample. On the basis of this pooled sample of 160 observations, the economist estimated the following linear equation:
Q = 40 - 1.1P + 1.5A + 0.32I + 0.5H + 0.1Pc
(2.5) (0.9) (0.6) (0.12) (0.17) (0.05)
R^2 = 0.91, SEE = 2.8, F = 311.30
Numbers in parenthesis are standard errors.
The variables and their forecasted values are:
Q=Quantity demanded (in thousands)
P=Average price (in Euro) =55;
A=Advertising expenditures (in thousands) = 20
I=Average household income (in thousands Euro) =31;
H=Total number of residential (house) sales (in thousands)=10;
Pc=Price of a leading competitor (in Euro)=50.
a. Should this company try to markets its toaster ovens in upscale gourmet shops where relatively high income level people shop? Explain using numbers!
b. How concerned should this company be about price discounts by its leading competitors? Explain using numbers?
c. Conduct a t-test to check the statistical validity of the estimated equation at 95 percent confidence.
d. Assuming the value of the variables are given, indicate 95 percent confidence interval of the forecast demand for toaster ovens. e. Among which variables you might expect multicolor linearity problem Explain briefly
Explanation / Answer
a) The demand equation for toaster oven
Q = 40 - 1.1P + 1.5A + 0.32I + 0.5H + 0.1Pc
The average household income is 31,000 euros
The demand at this income level
Q = 40 - 1.1X55+1.5X20,000+0.31X31,000+0.5X10,000+0.1X50 = 44,594.5 units
If the company markets the toaster oven in an upscale gourment shops where higher income level people shop and all other factors remaining the same
Let us assume the average upscale income level is 34,000 euros
The demand at this income level will be
Q = 40 - 1.1X55+1.5X20,000+0.31X34,000+0.5X10,000+0.1X50 =45,525 units
Hence it will advisable to market the toaster ovens in upscale gourment shops where higher income level people shop .
b) Suppose the competitors offer a 10% price discount. The price of the competitor product will be 45 Euros.
The demand of toaster oven at the revised competitor product price will be
Q = 40 - 1.1P + 1.5A + 0.32I + 0.5H + 0.1Pc
Q = 40 - 1.1X55+1.5X20,000+0.32X31,000+0.5X10,000+0.1X45
Q = 44,904
Hence the demand increases even if the competitors offer price discounts.
c) K = 5
n-k = 155 where n = sample size
H0 = The regression equation is not significant.
H1 = The regression equation is significant
By seeing the value in the F table for 95% confidence level.
The value of F = 2.21
Given value of F= 311.30
The computed value of F from table is 2.11which is less than 311.30
We can conclude the regession equation is significant.
d) H0 =The forecasted demand is not significant.
H1 = The forecasted demand is significant.
There are 5 independent variables in the demand equation.
we will take a sample size of 20
n-k = 20-5 = 15
The computed value of F from table will be 2.90
Hence the forecast demand is significant as the value from the table is 2.90 which is less than 311.30
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