Question 2

Deciding where to locate a new retail store is important. The manager of a chain of pizza shops plans to use a regression model to help select a location for a new shop. They decide to use annual gross revenue to measure success, which is the dependent variable. The manager believes that determinants of success include the following:

Number of people living within 1km of the store (PEOPLE)

Mean income of households within 1km of the store (INCOME)

Number of competitors within 1km of the store (COMPTORS)

The average price of a large pizza (PRICE)

Whether the store has street frontage or not (FRONTAGE), The manager randomly selects 50 pizza shops and records the values of each of the variables of interest. He proposes the following regression model:

Revenue People Income Comptors Price Frontage 323581 5556 42746 3 5.5 Yes 343682 5917 43106 2 6.0 No 375264 5483 46993 5 6.0 Yes 351242 6400 43249 2 5.0 Yes 328417 5917 40695 3 5.5 No 318069 6683 41253 3 5.5 No 330959 6065 40791 2 5.5 Yes 267236 7491 39932 3 5.5 No 320883 6284 36826 1 6.0 Yes 409535 5851 45300 3 6.0 Yes 316262 5681 42645 3 5.5 No 351806 5187 42306 2 6.0 Yes 333655 6164 44842 3 5.0 No 372679 7320 45233 3 6.0 Yes 362796 5062 41426 3 6.0 Yes 379442 6750 42606 1 6.0 Yes 287993 6229 37993 3 6.0 No 404099 6599 51518 3 5.0 Yes 356063 5986 45652 4 5.0 No 340394 6886 38076 4 5.5 No 344154 5416 39068 2 6.0 No 355700 6393 39822 4 5.5 No 312596 5359 37375 4 6.0 Yes 341242 7190 42597 3 5.0 Yes 299572 6397 37790 3 6.0 No 356589 6292 39984 2 6.0 Yes 333101 4379 41519 2 5.5 No 383161 6594 40169 2 6.0 Yes 376127 5719 44717 2 5.5 Yes 363707 5638 41820 4 5.0 No 348881 6056 39873 2 6.0 No 402021 5006 41547 2 6.0 Yes 377807 5071 43944 3 6.0 No 301863 4714 38304 2 5.5 No 374906 6513 47699 2 6.0 Yes 406527 5361 52626 4 6.0 Yes 256640 6320 34355 3 6.0 No 351003 7619 39437 3 5.0 Yes 310568 6727 39611 5 6.0 No 298355 6475 39409 4 6.0 No 346179 6008 38103 1 6.0 Yes 323096 3469 43168 2 5.5 Yes 301058 3172 39395 2 5.5 No 401811 6572 48638 5 5.5 Yes 385025 7999 38404 2 6.0 Yes 297707 4138 36357 3 6.0 No 385850 7607 43228 3 5.5 Yes 287799 5418 30999 1 5.5 No 387012 5927 47181 4 5.5 Yes 314170 5453 35821 3 5 5 Yes Question 2 (25 marks) Deciding where to locate a new retail store is an important decision. The manager of a chain of pizza shops plans to use a regression model to help select a location for a new shop. They decide to use annual gross revenue as a measure ofsuccess, which is the dependent variable, The manager believe that determinants of success include the following: Number of people living within 1km of the store (PEOPLE) Mean income of households within 1km of the store (INCOME) Number of competitors within 1km of the store (COMPTORS) Average price of a large pizza (PRICE) Whether the store has street frontage or not (FRONTAGEJ The manager randomly selects 50 pizza shops and records the values of each of the variables of interest. He proposes the following regression model: REVENUE = n + lPEOPLE + 311NCOME + zcomrons + mmrcE + SFRONTAGE + 2 Estimate this regression model. a b. Test the overall utility of the model. C. d 8 Which independent variables are linearly related to the revenue? Explain. . Interpret all the estimated coefficients. . What E the coefcient of determination and the coefcient of determination adjusted for degrees of freedom? What do these statistics tell you about the regression equation