Pittsburgh is the 26th largest metropolitan area in the United States. We are in
ID: 3319240 • Letter: P
Question
Pittsburgh is the 26th largest metropolitan area in the United States. We are interested in using the distance that a city is from Pittsburgh (in miles) to predict the driving time (in minutes) to the largest city in the 25 metropolitan area:s that are larger than Pittsburgh. Use the Hypothesis Test Workbook and data in Excel to generate the output and answer the following questions regarding the relationship between distance and travel time a. What is the value of the coefficient of determination? b. Interpret coefficient of determination in the context of the problem. c. What is the linear model? d. What is the equation of the regression line? e. Oklahoma City is 1100 miles away from Pittsburgh. Use the regression line to predict the number of minutes it would take to drive to Oklahoma City f. If it actually took you 1050 minutes to drive to Oklahoma City, did your trip go faster than expected or slower than expected according to the model? Explain why in terms of the residual Anchorage, Alaska is 4034 miles from Pittsburgh. Why it would be dangerous to use this model to predict how long it would take to drive to Anchorage? g.Explanation / Answer
a)
b1= nE(xy)-ExEy/nE(x2)-(Ex2)
=25*48017562-(30726*27064)/25*55025428-(30726*30726)
=0.85
b0=Ey-b1Ex/n
=27064-(0.85*30726)/25
=32.03
r (correlation)=n(Exy)-(Ex)(Ey)/(nEx2-(Ex)2)(nEy2-(Ey)2)
=25*48017562-(30726*27064)/ 25*55025428-(30726*30726)* 25*42439768-(27064*27064)
=0.98
r^2=0.98^2=0.96
b)
96% of the variation in the dependent variable is accounted for by the independent variable.
c and d)
Time=32.03+0.85x
e)
Time=32.03+0.85*1100=967.03
f)
Faster
g)
Because there are more chances of error when preducting a long distance and hence no accurate predictions
Metropolitan Area Travel Time (Minutes) (y) Distance (x) y^2 x^2 xy New York 416 371 173056 137641 154336 Los Angeles 2312 2427 5345344 5890329 5611224 Chicago 351 460 123201 211600 161460 Dallas 982 1229 964324 1510441 1206878 Houston 1519 1338 2307361 1790244 2032422 Washington DC 218 246 47524 60516 53628 Philadelphia 260 304 67600 92416 79040 Miami 1012 1175 1024144 1380625 1189100 Atlanta 578 685 334084 469225 395930 Boston 654 572 427716 327184 374088 San Francisco 2229 2577 4968441 6640929 5744133 Phoenix 1900 2058 3610000 4235364 3910200 Riverside 1756 2395 3083536 5736025 4205620 Detroit 230 286 52900 81796 65780 Seattle 2503 2523 6265009 6365529 6315069 Minneapolis 786 868 617796 753424 682248 San Diego 1932 2412 3732624 5817744 4659984 Tampa 708 1025 501264 1050625 725700 Denver 1221 1445 1490841 2088025 1764345 St. Louis 612 602 374544 362404 368424 Baltimore 237 248 56169 61504 58776 Charlotte 430 448 184900 200704 192640 Orlando 935 970 874225 940900 906950 San Antonio 1181 1497 1394761 2241009 1767957 Portland 2102 2565 4418404 6579225 5391630 Sum Sum Sum Sum Sum 27064 30726 42439768 55025428 48017562 SUMMARY OUTPUT Regression Statistics Multiple R 0.98 R Square 0.96 Adjusted R Square 0.96 Standard Error 151.73 Observations 25 ANOVA df SS MS F Significance F Regression 1 12611835.76 12611835.76 547.79 0.00 Residual 23 529528.40 23022.97 Total 24 13141364.16 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 32.03 54.18 0.59 0.56 -80.06 144.11 Distance (x) 0.85 0.04 23.40 0.00 0.78 0.93