1.Regress Sales (dependent variable) linearly versus independent variables P, A, CP, I, P, T. Report your results.
2.Based on economic theory, what signs would you expect these coefficients have? Do they have the hypothesized signs? Which of the variables are statistically significant (different from zero) at the 95 percent confidence level?
3.Now use this data to estimate the multiplicative form of this demand model (use the same dependent and independent variables). Report your results.
4.Compare the statistical properties of your multiplicative model with the linear model. Which fits the data better? Explain why.
5.What is your estimate of the price elasticity of demand (P), income elasticity of demand (I), and cross price elasticity of demand (CP) in the multiplicative model? Compare these elasticity estimates with the corresponding elasticities in the linear model when calculated at mean values for each variable.
6.In the multiplicative model perform a statistical test to determine whether demand is elastic, interest rates are a complement good, and if new car sales are a normal good at the 95 percent confidence level.
7.Forecast Jim's Steaks sales during a year in which the price (P) is $6.50, Advertising Expenditures (A) is $29,900, Competitors' Price (CP) is $6.70, Income (I) is $52,000, Population (P) is 7,300,000. Time (T) is 9. Derive a 95 percent confidence interval around this forecast.
8.Use the demand elasticities from your multiplicative model to analyze the impact of the following management decisions:
a)If Jim's Cheesesteak's competitor lowers price by 10 percent how will this impact Jim's sales (percentage change)? To offset this Jim's Steaks strategically cuts price by 2 percent. Does this strategy work? Explain.
Jim's Cheesesteaks Regional Market Demand Data, 2018-1 to 2019-4 Advertising Price Expenditures Competitors' Unit Sales (Q) ($) ($) Price ($) Income ($) Population Time Variable In Q In P In A In Pc In I In Pop In T 193,334 6.90 15,827 7.40 48.421 5,055,856 1 12.172175 1.9315214 9.6694726 2.00148 10.787689 15.436058 0 170,041 7.79 20,819 5.18 49,038 5,091,361 2 12.043795 2.0528409 9.9436213 1.64480506 10.800351 15.443056 0.6931472 247,709 6.21 14,062 5.65 49.663 5,127,1 15 3 12.42001 1.8261609 9.5512314 1.73165555 10.813015 15.450054 1.0986123 183.259 7.29 16,973 6.60 50,296 5,163,120 4 12.118656 1.9865035 9.7393791 1.88706965 10.825681 15.457052 1.3862944 282,118 6.87 18,815 6.81 50.938 5,199,378 5 12.550081 1.9271641 9.8424097 1.91839212 10.838364 15.46405 1.6094379 203,396 6.46 14,176 5.22 51,587 5,235,891 6 12.22291 1.8656293 9.5593057 1.6524974 10.851025 15.471048 1.7917595 167,447 7.17 17,030 5.59 52,245 5,272,660 7 12.028422 1.9699057 9.7427318 1.72097929 10.863699 15.478046 1.9459101 361,677 5.72 14,456 6.21 52,911 5,309,688 8 12.798507 1.7439688 9.5788648 1.8261609 10.876367 15.485044 2.0794415 401,805 6.57 27,183 5.34 50,456 ,509,448 1 12.903722 1.8825138 10.210347 1.67522565 10.828857 16.067796 0 412,312 6.62 27,572 6.56 51,100 9,526,087 2 12.929536 1.8900954 10.224556 1.8809906 10.84154 16.069545 0.6931472 321,972 7.82 34.367 6.23 51,751 9,542,755 3 12.68222 2.0566846 10.444852 1.82937633 10.854199 16.071293 1.0986123 445,236 6.57 26,895 6.47 52,411 9,559,452 4 13.00636 1.8825138 10.199696 1.86717611 10.866872 16.073041 1.3862944 479,713 6.91 30,539 5.75 53,079 9,576,178 5 13.080943 1.9329696 10.32676 1.74919985 10.879537 16.074789 1.6094379 459,379 6.48 26,679 5.20 53,756 9,592,933 6 13.037631 1.8687205 10.191632 1.64865863 10.892211 16.076537 1.7917595 444,040 6.44 26,607 5.66 54,441 9,609,718 7 13.00367 1.8625285 10.18893 1.73342389 10.904873 16.078285 1.9459101 376,046 7.79 32,760 5.23 55,136 9,626,532 8 12.837467 2.0528409 10.396964 1.65441128 10.917558 16.080034 2.0794415 255,203 7.07 19,880 7.46 44,249 5,952,784 1 12.449815 1.9558605 9.8974695 2.00955541 10.697588 15.59937 0 270,881 5.60 19,151 6.69 44,813 5,986,874 2 12.509435 1.8870696 9.8601102 1.90061387 10.710254 15.60508 0.6931472 330,271 6.07 15,743 6.45 45,385 6,021,160 3 12.707669 1.8033586 9.6641511 1.86408013 10.722937 15.61079 1.0986123 313,485 6.54 17,512 5.44 45,963 6,055,642 4 12.655507 1.8779372 9.7706416 1.69377906 10.735592 15.616501 1.3862944 311,500 6.30 16,984 5.66 46,549 6,090,322 5 12.649155 1.8405496 9.740027 1.73342389 10.748261 15.622212 1.6094379 370,780 5.81 15,698 6.62 47,143 6,125,200 6 12.823364 1.7595806 9.6612886 1.89009537 10.760941 15.627922 1.7917595 152,338 8.00 22,057 7.43 47,744 6,160,278 7 11.933857 2.0794415 10.001385 2.00552586 10.773609 15.633632 1.9459101 320,804 6.69 17,460 6.83 48,353 6,195,557 8 12.678586 1.9006139 9.7676678 1.92132467 10.786284 15.639343 2.0794415 738,760 6.21 42,925 5.93 53,929 13,030,242 1 13.512728 1.8261609 10.66721 1.78002421 10.895424 16.382784 0 707,015 7.14 50,299 7.20 54,617 13,057,136 2 13.468807 1.9657128 10.82574 1.97408103 10.9081 16.384845 0.6931472 699,051 5.43 37,364 5.39 55,313 13,084,085 3 13.457479 1.6919391 10.528463 1.68454538 10.920763 16.386907 1.0986123 628,838 7.30 50,602 4.93 56,018 13,111,090 4 13.351629 1.9878743 10.831746 1.59533899 10.933428 16.388969 1.3862944 631,934 7.60 53,562 6.26 56,732 13,138,151 5 13.35654 2.0281482 10.888595 1.83418019 10.946094 16.391031 1.6094379 651,162 7.24 48,911 6.02 57,456 13,165,267 6 13.386514 1.9796212 10.797758 1.79508726 10.958775 16.393093 1.7917595 765,124 7.06 49,422 7.43 58,188 13,192,440 7 13.547793 1.9544451 10.808151 2.00552586 10.971434 16.395154 1.9459101 741,364 6.19 44,061 6.82 58,930 13,219,669 8 13.516247 1.8229351 10.69333 1.91985947 10.984106 16.397216 2.0794415 291,773 5.78 13,896 6.18 58,959 3,176,146 1 12.583731 1.7544037 9.5393563 1.82131827 10.984598 14.971179 0 153,018 6.84 27,429 5.06 59,711 3,184,576 2 11.938311 1.9227877 10.219356 1.62136648 10.997272 14.97383 0.6931472 574,486 6.42 31,631 7.17 60,472 3,193,029 3 13.261231 1.8594181 10.361893 1.96990565 11.009936 14.976481 1.0986123 75,396 7.56 39,176 4.90 61,243 3,201,504 4 11.23051 2.0228712 10.57582 1.58923521 11.022605 14.979131 1.3862944 590,190 5.61 33,538 5.53 62,024 3,210,002 5 13.2882 1.7245507 10.420434 1.71018782 11.035277 14.981782 1.6094379 288,112 7.58 53,643 5.51 62,815 3,218,522 6 12.571 105 2.0255132 10.890106 1.70656462 11.047949 14.984433 1.7917595 276,619 7.58 60,284 5.84 63,616 3,227,065 7 12.530396 2.0255132 11.006822 1.7647308 11.06062 14.987084 1.9459101 522,446 5.65 53,595 6.48 64,427 3,235,630 8 13.166277 1.7316555 10.889211 1.86872051 11.073288 14.989734 2.0794415 395,251 6.75 29,990 6.11 53,547 7,430,764
