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Advertising and price as determinants of sales

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Sam Smith, owner and general manager of Campus Stationery Store, is concerned about the sales behavior of a scanner at the store. He understands that there may be many factors, which may help explain sales, but he believes that advertising and price are major determinants of sales. Sam collects the data given below with:
Y = SALES (# of sales)
X1 = ADS (# of ads)
X2 = PRICE ($)

SALES ADS PRICE Predict ADS Predict PRICE
33 3 125 10 130
61 6 115
70 10 113
82 13 130
17 9 145
24 6 140
40 5 120
48 5 116
56 7 110
72 11 108

Regression Analysis: sales versus ads, price

The regression equation is:
sales = 157 + 4.33 ads - 1.14 price

Predictor Coef SE Coef T P
Constant 157.50 33.78 4.66 0.002
ADS 4.327 1.078 4.01 0.005
PRICE -1.1428 0.2677 -4.27 0.004

S = 10.1422 R-Sq = 82.9% R-Sq(adj) = 78.1%

Analysis of Variance:

Source DF SS MS F P
Regression 2 3502.0 1751.0 17.02 0.002
Residual Error 7 720.1 102.9
Total 9 4222.1

Predicted Values for New Observations

New Obs Fit SE Fit 95% CI 95% PI
1 52.20 4.67 (41.16, 63.25) (25.80, 78.61)

Values of Predictors for New Observations

New Obs ADS PRICE
1 10.0 130

Correlations: SALES, ADS, PRICE

SALES ADS
ADS 0.621
0.055

PRICE -0.661 0.008
0.037 0.982

Cell Contents: Pearson correlation
P-Value

a. Analyze the above output to determine the multiple regression equation
b. Find and interpret the multiple index of determination (R-Sq)
c. Perform the t-tests on ???? ? 1 and on ???? ? 2 (Use two tailed test with (??= 0.05). Interpret your results
d. Predict the number of sales given that there were 10 ads and the price was $130; use both a point estimate and the appropriate interval estimate

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Solution Summary

Advertising and price as determinants of sales

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See Also This Related BrainMass Solution

Offer, Acceptance and Contract Formation

Help with this problem:

1. Analysis and applicable rules as applied to the seller/advertiser.
2. Analysis and applicable rules as they apply to the purchaser.

PROBLEM:

A store ran a sales promotion to boost sales of a product. The promotion included both free gifts for purchases and low interest financing. It was supported by a print advertising campaign in several states.

The advertisements ran in major daily newspapers, and stated as follows:

Buy this product at a low price of $14,599.00. We will finance it an incredible 7.5% interest rate** and let you pick the term of the loan: 6, 12, or 18 months. No monthly payments. At the end of the term you pay:

6 months: $14, 781.49
12 months: $14, 963.98
18 months: $15, 146.46 ** Annual Percentage Rate: Subject to credit qualification.

Plus we will help you get started with a gift certificate that can be redeemed for products worth $300.00.

The promotion was successful, with 68 of the products sold in 2 weeks. All 68 gift certificates were issued and have been fully redeemed by all the customers. Unfortunately the advertisements contained a serious error. A financial analyst calculated the financing figures for the ad using a 2.5% interest rate, not a 7.7% interest rate. The numbers is the advertisements were incorrect. The correct numbers based on a 7.5% interest rate are:

6 months: $15,146.46
12 months: $15,693,93
18 months: $16,241.39

Total Loss on all Contracts: $65,695.50

Customers who bought the product during the promotion signed standard plain language promissory notes that clearly stated the 7.5% interest rate. Only one person selected the 6 month term, 22 selected the 12 month term , and 45 selected the 18 month term. The customer with the 6 month term came forward and a dispute arose over the correct amount due. The seller believes they are entitled to the higher amount, but the customer refused to pay more than the advertised amount. To resolve the matter, the smaller amount was accepted for this one case with a six month term, but do not wish to accept the advertised amount on the remaining 67 contracts with 12 or 18 month contracts.

Help determining if the seller is contractually bound by the terms of the advertisement, or whether they can enforce the contract terms of the promissory notes for the higher amount.

Help with all legal arguments for the seller and purchaser. This does not involve the law of mistakes.

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