16.5 To help determine how many beers to stock the concession manager at Yankee Stadium wanted to know how the temperature affected beer sales. Accordingly she took a sample of 10 games and recorded the number of beers sold and the temperature in the middle of the game. Temperature Beers 80 20 533 68 1 439 78 13 829 79 21 286 87 30 985 74 17 187 86 30 240 92 37 596 77 9 610 84 28 742 a. Compute the coefficients of the regression line. b. Interpret the coefficients. 16.7 Florida Condominiums are popular winter retreats for many North Americans. In recent years the prices have steadily increased. A real estate agent wanted to know why prices of similar-sized apartment in the same building vary. A possible answer lies in the floor. It may be that the higher the floor the greater the sale price of the apartment. He recorded the price (in $1 000’s) of 1 200 sq. ft. condominiums in several buildings in the same location that have sold recently and the floor number of the condominium. a. Determine the regression line. b. What do the coefficients tell you about the relationship between the two variables? Floor Price 22 212 20 225 16 261 4 184 18 232 18 222 21 210 13 201 14 189 8 200 4 203 2 196 16 220 13 245 12 211 8 216 21 256 7 173 8 194 8 196 23 182 21 230 10 216 9 188 15 210 1 216 27 218 8 169 27 235 8 227 10 191 1 203 27 223 14 206 28 204 4 190 28 246 8 168 10 193 12 186 7 193 27 224 21 231 6 183 21 224 9 212 12 232 7 193 18 233 12 249 16.105 Mutual funds minimize risk by diversifying investments they make. There are mutual funds that specialize in particular types of investments. For example the TD Precious Metal Mutual Fund buys shares in gold-mining companies. The value of this mutual fund depends on a number of factors related to the companies in which the fund invests as well as on the price of gold. To investigate the relationship between the value of the fund and the price of gold an MBA STUDENT GATHERED THE DAILY FUND PRICE AND THE DAILY PRICE OF GOLD FOR A 28-DAY PERIOD. Can we infer from these data that there is a positive linear relationship between the value of the fund and the price of gold? Fund Gold 11.15 375.97 11.28 373.03 10.25 365.51 12.10 382.19 11.55 377.25 11.45 373.96 12.00 371.32 12.64 365.26 12.02 380.34 11.23 366.83 11.26 375.02 13.04 381.86 12.39 386.04 12.62 384.43 11.92 374.30 10.90 361.20 13.04 389.19 11.51 374.24 13.34 393.75 12.27 376.82 11.64 380.77 11.24 367.60 10.60 367.64 11.28 367.23 11.77 372.60 11.24 375.18 12.58 380.66 9.21 358.06 16.107 A computer dating service typically asks for various pieces of information such as height weight and income. One such service requested the length of index fingers. The only plausible reason for this request is to act as a proxy on height. Women have often complained that men lie about their heights. If there is a strong relationship between heights and index fingers the information can be used to “correct” false claims about heights. To test the relationship between the two variables researchers gathered the heights and lengths of index fingers (in centimeters) of 121 students. a. Graph the relationship between the two variables. b. Is there sufficient evidence to infer that height and length of index fingers are linearly related? c. Predict with 95% confidence that height of someone whose index finger is 6.5 cm long. Is this prediction likely to be useful? Explain Height (cm) Index finger length (cm) Gender 154.9 5.8 0 154.9 6.1 0 154.9 6.1 0 154.9 6.8 0 154.9 6.9 0 154.9 7.2 0 155.0 6.3 0 155.0 6.6 0 155.0 7.3 0 156.2 6.0 0 157.5 4.8 0 157.5 6.6 0 157.5 6.7 0 157.5 6.7 0 160.0 6.4 0 160.0 6.4 0 160.0 6.5 0 161.3 7.1 0 162.6 6.0 0 162.6 6.1 0 162.6 6.5 0 162.6 6.8 0 162.6 7.0 0 162.6 7.0 0 162.6 7.4 0 162.6 7.5 0 163.0 6.6 0 163.5 6.7 0 163.8 6.4 0 165.0 7.2 0 165.1 5.0 0 165.1 6.4 0 165.1 6.6 0 165.1 6.8 0 165.1 7.1 0 165.1 7.5 0 165.1 8.0 1 165.1 8.3 0 166.0 6.9 0 166.4 7.0 0 166.4 7.0 1 166.4 7.4 0 167.6 6.4 1 167.6 6.5 0 167.6 7.3 0 167.6 7.5 0 167.6 7.6 0 167.6 8.5 0 168.4 6.5 1 168.9 6.8 1 170.0 7.9 1 170.2 5.8 1 170.2 7.1 1 170.2 7.5 1 170.2 7.5 1 170.3 7.8 0 171.5 7.5 1 172.1 7.6 1 172.7 7.3 0 172.7 7.5 1 172.7 7.9 1 172.7 8.2 1 172.7 9.0 0 173.0 7.2 1 174.5 7.7 1 174.6 7.4 1 175.3 6.6 0 175.3 7.0 1 175.3 7.0 1 175.3 7.1 0 175.3 7.2 1 175.3 7.5 1 175.3 7.5 1 175.3 7.6 1 175.3 8.0 1 175.3 8.1 1 176.4 7.6 1 176.5 6.4 1 176.5 7.0 1 176.5 7.1 1 177.8 6.8 1 177.8 7.4 1 177.8 7.8 0 177.8 8.1 1 177.8 8.2 1 178.2 7.6 1 179.1 7.0 1 179.1 7.5 0 179.1 7.6 1 180.0 7.9 1 180.1 8.5 1 180.3 5.7 1 180.3 7.1 0 180.3 7.1 1 180.3 7.5 1 180.3 7.8 1 180.3 7.8 1 180.3 7.9 1 180.3 9.0 1 180.4 8.4 1 181.7 8.3 1 181.8 7.8 1 181.9 7.6 1 182.9 6.9 1 182.9 7.0 1 182.9 7.5 1 182.9 9.0 1 185.0 7.9 1 185.4 7.1 1 185.4 7.3 1 185.4 7.6 1 185.4 8.0 1 185.4 8.3 1 186.7 7.3 1 187.5 8.0 1 188.0 7.1 1 188.0 8.5 1 188.3 8.3 1 190.5 7.5 1 191.0 8.2 1 191.4 8.0 1 17.3 The president of a company that manufactures drywall wants to analyze the variables that affect demand for his product. Drywall is used to construct walls in houses and offices. Consequently the president decides to develop a regression model in which the dependent variable is monthly sales of drywall (in hundreds of 4×8 sheets and the independent variables are Number of building permits issued in the county Five year mortgage rates (in percentage points) Vacancy rate in apartments (in percentage points) To estimate a multiple regression model he took monthly observations from the past 2 years. a. Analyze the data using multiple regression b. What is the standard error of estimate? Can you use this statistic to assess the model’s fit? If so how? c. What is the coefficient of determination and what does it tell you about the regression model? d. Test the overall validity of the model e. Interpret each of the coefficients f. Test to determine whether each of the independent variables is linearly related to drywall demand in this model g. Predict next month’s drywall sales with 95% confidence if the number of building permits is 50 the 5-year mortgage rate is 9.0% and the vacancy rates are 3.6% in apartments and 14.3% in office buildings. Drywall Permits Mortgage A Vacancy O Vacancy 328 49 8.35 2.98 13.43 376 79 8.08 5.6 14.51 373 79 7.9 2.25 14.24 144 50 7.69 4.26 14.3 194 37 7 2.6 11.64 220 53 7.32 2.97 10.61 126 22 8.4 5.35 18.45 301 69 8.28 3.13 18.52 54 21 8 5.6 10.29 252 46 8.95 4.81 11.91 381 79 8.21 5.88 17.75 173 30 7.24 2.98 18.16 152 38 7.35 5.69 17.14 351 73 7.27 4.86 16.11 233 55 7.08 5.68 18.54 35 12 7.76 4.46 19.46 290 62 8.21 2.23 19.26 5 12 7.76 5 17.28 335 60 7.2 2.42 15.15 280 49 7.57 3.25 19.94 101 14 8.44 3.61 15.47 297 66 8.43 2.13 12.75 309 62 8.14 4.35 12.24 233 40 8.81 2.31 18.65
