# 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.

- Use regression to estimate the demand function. Show the results.
- Write the subsequent demand equation, with Qd as the dependent variable; Price, Advertising, Product Development, and Rel Price as the independent variables.
- 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.
- Which variable is most important in determining quantity demanded? Justify the reasoning?
- 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 |

- 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.

- Forecast Qd if:

{` Price $10.00 Advertising $150,000 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 Adv = dollars spend in advertising, that quarter Prod Dev = dollars spent in product development that quarter. Product development should be thought of as money spent on developing additional features or properties that make the product more desirable in the eyes of customers. Rel Price = Price of a related product `}