# Use regression to estimate the demand function

Extended Problem with Chapter 4

Complete the following questions using the spreadsheet, “ ExtendedProblems Data.” Begin by entering the data provided on a separate Excel spreadsheet and label the tab “handout.” Complete the following steps for this assignment.

1. Use regression to estimate the demand function. Show the results.
2. Write the subsequent demand equation, with Qd as the dependent variable; Price, Advertising, Product Development, and Rel Price as the independent variables.
3. How strong is the relationship between the quantity demanded and the set of independent variables? List and briefly interpret at least two measures of this strength.
4. Which variable is most important in determining quantity demanded? Justify the reasoning?
5. Solve for the price elasticity of demand. Classify the product’s demand as elastic or inelastic. Price elasticity of demand can be found by the following equation:
 ep = (coefficient of price variable x average price) / (average Qd) Average values for all variables are below. Qd 626,271 Price \$ 10.06 Advertising \$181,000 Product Development \$125,417 Rel Price \$10.16
1. Solve for the cross price elasticity of demand. Classify the relationship between these products as complements or substitutes. The formula for this coefficient is similar to the one for price elasticity:

Ex: (coefficient of Rel Price variable x average value of Rel price)/(average Qd)

The average variable levels are listed in part (f) above.

1. Forecast Qd if:
```{`
Price                   \$10.00
Product Development     \$150,000
Rel Price               \$10.25
`}```

Construct a 95% confidence interval around this forecast.

Data

The following sales and marketing data was accumulated by a manufacturer over the past 12 quarters.

```{`
Qd	         Price	         Adv	         Prod Dev	 Rel Price
561,628 	 \$9.75 	         \$150,000 	 \$115,000 	 \$9.46
697,734 	 \$9.25 	         \$162,000 	 \$100,000 	 \$9.44
761,217 	 \$9.40 	         \$125,000 	 \$125,000 	 \$10.14
667,994 	 \$10.25 	 \$250,000 	 \$100,000 	 \$10.09
496,985 	 \$10.40 	 \$200,000 	 \$150,000 	 \$10.21
637,148 	 \$9.90 	         \$160,000 	 \$120,000 	 \$10.16
569,773 	 \$10.55 	 \$250,000 	 \$100,000 	 \$10.34
663,146 	 \$10.17 	 \$245,000 	 \$115,000 	 \$10.31
432,424 	 \$10.30 	 \$185,000 	 \$140,000 	 \$10.52
535,571 	 \$10.50 	 \$140,000 	 \$150,000 	 \$10.56
698,376 	 \$10.20 	 \$185,000 	 \$140,000 	 \$10.38
793,260 	 \$10.00 	 \$120,000 	 \$ 150,000 	 \$10.32
`}```

Variable Definitions:

```{`Qd = quantity demanded, in units
Price = price per unit charged by the firm that quarter