# Business MathDemand and Regression Analysis

#### rr2013

##### New member

Branded Products, Inc., based in Halfway Tree is a leading producer and marketer of household laundry detergent and bleach products. About a year ago, Branded products rolled out its new Super Detergent in four western parishes, following success in more limited test markets. At the time of introduction, management wondered whether the company could successfully crack this market, dominated by Breeze and other major players. The following regression model forecast results for Super Detergent over the past seven months (30 weeks). The t-statistics are in parenthesis.
Q = 867.98 – 81.86P + 0.007A + 0.006I + 82.86Px + 1.309T
(345) (24) (0.7) (0.2) (18) (0.063)
R2 = 91.47%, Standard of Error of the Estimate = 33.64 t(0.01, (n-k)df) = 2.492, F(k-1, n-k, 0.01) = 3.895
Q is the demand in cases, P is tile price (per case), Px is the competitor price, A is advertising expenditures (in thousands of dollars), I is disposable income per capita (in thousands of dollars) and T represent the month.
If P = $700.5, Px =$750 A= $350,000 I =$900,000

1.What is the revenue implication for Branded Products, if there a recession? If there is a recession income will be affected(reduced) and this reduce revenue; a 302.24 reduction- (dervived from subtracting t-test values- 345-(24+.7+18+0-0.063)

2.What proportion of the variation in super detergent sales is explained by the regression model?
91.47%

3.Determine if Branded products should be concerned about its main competitors
yes any change in comptetirs price will affect barnded products revenue by 18%

4.If Branded Products wants to maintain at least its share of the market, what change in the price of their detergent will be necessary to compensate for a \$100 decrease in the price of its main competitors’ detergent?$700-$700*18%=$574

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#### Klaas van Aarsen

##### MHB Seeker
Staff member
Welcome to MHB, rr2013!

Branded Products, Inc., based in Halfway Tree is a leading producer and marketer of household laundry detergent and bleach products. About a year ago, Branded products rolled out its new Super Detergent in four western parishes, following success in more limited test markets. At the time of introduction, management wondered whether the company could successfully crack this market, dominated by Breeze and other major players. The following regression model forecast results for Super Detergent over the past seven months (30 weeks). The t-statistics are in parenthesis.
Q = 867.98 – 81.86P + 0.007A + 0.006I + 82.86Px + 1.309T
(345) (24) (0.7) (0.2) (18) (0.063)
R2 = 91.47%, Standard of Error of the Estimate = 33.64 t(0.01, (n-k)df) = 2.492, F(k-1, n-k, 0.01) = 3.895
Q is the demand in cases, P is tile price (per case), Px is the competitor price, A is advertising expenditures (in thousands of dollars), I is disposable income per capita (in thousands of dollars) and T represent the month.
If P = $700.5, Px =$750 A= $350,000 I =$900,000

1.What is the revenue implication for Branded Products, if there a recession? If there is a recession income will be affected(reduced) and this reduce revenue; a 302.24 reduction- (dervived from subtracting t-test values- 345-(24+.7+18+0-0.063)
I'm not sure what you're doing here.
You can't use t-values this way.
It seems to me that to predict the impact of a recession, we wouldn't assume a change in our own price, nor the competitor's price, advertising expenditures, or the month.
We would assume a change in the disposable income per capita...

2.What proportion of the variation in super detergent sales is explained by the regression model?
91.47%
Right.

3.Determine if Branded products should be concerned about its main competitors
yes any change in comptetirs price will affect barnded products revenue by 18%
How did you get that?

4.If Branded Products wants to maintain at least its share of the market, what change in the price of their detergent will be necessary to compensate for a \$100 decrease in the price of its main competitors’ detergent?$700-$700*18%=$574
How did you get that?

Maintaining the share of the market implies there should be no change in quantity.
That does not seem to be what you are doing.

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#### rr2013

##### New member
Welcome to MHB, yaoming988!

I'm not sure what you're doing here.
You can't use t-values this way.
It seems to me that to predict the impact of a recession, we wouldn't assume a change in our own price, nor the competitor's price, advertising expenditures, or the month.
We would assume a change in the disposable income per capita...

Right.

How did you get that?

How did you get that?

Maintaining the share of the market implies there should be no change in quantity.
That does not seem to be what you are doing.
Quote - regarding question one I subtracted the t values of all the factors excluding income - i saw something similar done in an example online but I'm not certain I'm on the right track please guide me in answering this question.

thr truth is i'm sure i should be using the values given to answer the questions i.ethe t test, f test, rsquared etc but i do not know how to go about doing that. The examples we work in class are a lot simplier.

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Quote - regarding question one I subtracted the t values of all the factors excluding income - i saw something similar done in an example online but I'm not certain I'm on the right track please guide me in answering this question.

thr truth is i'm sure i should be using the values given to answer the questions i.ethe t test, f test, rsquared etc but i do not know how to go about doing that. The examples we work in class are a lot simplier.