Question

Suppose the Kalamazoo Brewing Company (KBC) currently sells its microbrews in a seven-state area: Illinois, Indiana, Michigan, Minnesota, Mississippi, Ohio, and Wisconsin. The company’s marketing department has collected data from its distributors in each state. These data consist of the quantity and price (per case) of microbrews sold in each state, as well as the average income (in thousands of dollars) of consumers living in various regions of each state. The data for each state are available online at www.mhhe.com/baye8e under the filename $\mathit{Q}\mathbf{19}\mathbf{.}\mathit{x}\mathit{l}\mathit{s}$, where there are multiple tabs at the bottom of the spreadsheet, each referring to one of the seven states selling the Kalamazoo Brewing Company’s microbrews. Assuming that the underlying demand relation is a linear function of price and income, use your spreadsheet program to obtain least squares estimates of the state’s demand for KBC microbrews. Print the regression output and provide an economic interpretation of the regression results.

Short answer

Regression analysis is done by using the spreadsheet program.

Step-by-step solution

Do the regression analysis

Regression equation is given as follows:

$Q_m^d=a+b{P}_m+cM+e$

Obtain least square estimates

After the given procedure, we read the values of the coefficients from the obtained table and thus obtain least square estimates of the state's demand for KBC microbrews:

$Q_m^d\left(\text{Indiana}\right)=97.53-2.52P_m+2.11\mathrm{M}$

$\left.Q_m^d\text{( Illinois}\right)=-42.65+2.62P_m+14.32M$

$Q_m^d\left(\text{Michigan}\right)=182.44-1.02P_m+1.41\mathrm{M}$

$Q_m^d\left(\text{Minnesota}\right)=81.7-0.12P_m+3.41\mathrm{M}$

$Q_m^d\left(\text{Ohio}\right)=111.06-2.48P_m+7.03M$

$Q_m^d\left(\text{Wisconsin}\right)=107.6-1.94P_m+10.1\mathrm{M}$