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Explain how regression analysis may be used to estimate demand functions, and how to interpret and use the output of a regression. Try these problems: 7, 20

Short Answer

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To estimate demand, regression analysis might be employed.

Step by step solution

01

Introduction

The regression analysis is a statistical concept, which is highly useful in business. It works when business want to forecast its business scenarios.

02

Product’s Demand Elasticity:

The following are some of the elements that determine a product's demand elasticity: To estimate demand, regression analysis might be employed. Assume we have information on the number of units demanded for a particular commodity at various pricing levels. This can be simulated to determine the good's demand function.

We may fit a model with the quantity demanded as the dependent variable and price as the independent variable in this situation. The formula will be as follows:Q=a-bP

Where Q stands for quantity and P stands for price." a" and " b" are now the coefficients.

In this equation, "a" represents autonomous demand that exists regardless of price, and "b" represents the amount by which autonomous demand exists.

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Most popular questions from this chapter

You are a division manager at Toyota. If your marketing department estimates that the semi-annual demand for the Highlander isQ-150,000-1.5P, what price should you charge in order to maximize revenues from sales of the Highlander?

The demand function for good X is Qxd=a+bPx+cM+e', where role="math" localid="1657355528456" Pxis the price of good Xand Mis income. Least squares regression reveals that a^=8.27,b^=-2.14;andc^=0.36,ฯƒa^=5.32;ฯƒb^=0.41;andฯƒc^=0.22. The R-squared=0.35..

a. Compute the t-statistic for each of the estimated coefficients.

b. Determine which (if any) of the estimated coefficients are statistically different from zero.

c. Explain, in plain words, what the R-square in this regression indicates.

Apply various elasticities of demand as a quantitative tool to forecast changes in revenues, prices, and/or units sold.

As the owner of Barneyโ€™s Broilersโ€”a fast-food chainโ€”you see an increase in the demand for broiled chicken as consumers become more health conscious and reduce their consumption of beef and fried foods. As a result, you believe it is necessary to purchase another oven to meet the increased demand. To finance the oven, you go to the bank seeking a loan. The loan officer tells you that your revenues of\(750,000 are insufficient to support additional debt. To qualify for the loan, Barneyโ€™s Broilersโ€™s revenue would need to be\)50,000 higher. In developing a strategy to generate the additional revenue, you collect data on the price (in cents) per pound you charge customers and the related quantity of chicken consumed per year in pounds. This information is contained in the file called Q18.xls available online at www.mhhe.com/baye8e. Use these data and a log-linear demand specification to obtain least squares estimates of the demand for broiled chicken. Write an equation that summarizes the demand for broiled chicken, and then determine the percentage price increase or decrease that is needed in order to boost revenues by$50,000 .

As newly appointed โ€œEnergy Czar,โ€ your goal is to reduce the total demand for residential heating fuel in your state. You must choose one of three legislative proposals designed to accomplish this goal: (a) a tax that would effectively increase the price of residential heating fuel by \(1; (b) a subsidy that would effectively reduce the price of natural gas by\)3; or (c) a tax that would effectively increase the price of electricity (produced by hydroelectric facilities) by$4 . To assist you in your decision, an economist in your office has estimated the demand for residential heating fuel using a linear demand specification. The regression results are presented on page 119. Based on this information, which proposal would you favor? Explain.

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