Exam 6: Multiple Linear Regression Analysis

Figure: Suppose you regress the self-reported number of cigarettes smoked per day on Age,Family Size,and Years of Education and that you get the results in Figure 6.2. SUMMARY OUTPUT Regression Statistier Multiple R 0.070494476 R Square 0.004969471 Adpasted R Square 0.001879314 Standard Error 4.819403326 Observations 970 ANOVA df SS MS F Significance F Regression 3 112.0566012 37.3522004 1.608161442 0.185858614 Residual 966 22436.94237 23.22664841 Total 969 22548.99897 Coefficients Standard Error t Stat P-value Lower 9396 Upper 95\% Intercept 4.049920982 1.042107341 3.886280064 0.000108739 2.004865844 6.094976119 Age 0.015626984 0.010365497 1.507596119 0.131984878 -0.004714504 0.035968471 Family Sire -0.093093463 0.084602383 -1.100364552 0.271447442 -0.259119103 0.072932177 Years of Education 0.005642075 0.06474525 0.087142685 0.930576157 -0.121415476 0.132699626 $\text { Figure } 6.2$ -Based on the estimates in Figure 6.2,you should conclude that,holding all other independent variables constant,each additional family member is estimated to be associated with

Figure: Suppose you regress the number of medals won by countries in the 1996,2000,2004,and 2008 Olympics on GDP Per Capita (Thousands),Population (Millions),and Olympic Year and that you get the results in Figure 6.1. SUMMARY OUTPUT Regression Statisties Multiple R 0.473932054 R Square 0.224611592 Adyasted R Square 0.218853757 Standerd Error 14.85665558 Observations 408 ANOVA ff SS MS F Sigejficance F Regressice 3 25830.70959 8610.236529 39.00973242 3.69997E-22 Residual 404 89170.96688 220.7202151 Total 407 115001.6765 Coefficients Standand Error t Stat P-value Lower 95\% Upper 95\% Intercept 385.4384477 338.9966744 1.136997725 0.25621316 -280.9792491 1051.856144 GDP Per Capita (Thousands) 0.28651666 0.046941033 6.103756974 2.4315-09 0.194237479 0.37879584 Popplasion (Milions) 0.041979674 0.00443387 9.467954334 2.42102-19 0.033263338 0.050696011 Year -0.191084928 0.169402339 -1.127994491 0.259991678 -0.524105098 0.141935242 $\text { Figure } 6.1$ -Based on the estimates in Figure 6.1,you should conclude that a 1 million increase in population is estimated to be associated with

How does the Adjusted R-squared differ from the R-squared? Why would the Adjusted R-squared be preferred to the R-squared?

Suppose you are interested in determining the factors that determine the number of crimes committed on campus.To this end,you collect data from 75 colleges on number of crimes per students enrolled,number of police officers per students,unemployment rate,tuition,and the percentage of male students.You run a regression and obtain the following results $Crime~ \hat{per }~Student = 35 - 15$ Police per Student $- .24$ Tuition (13) (4) $~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~$ (.07) $+ 3$ Unemployment Rate $+ 8$ Percent Male $( 2.5 )$$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~$ (5) =75 =.2305 a)Which of the coefficient estimates are statistically significant at the 5% level? b)You run an additional regression in order to jointly test if two coefficients are equal to 0.State the hypothesis,calculate the test statistic,state the regression rule,and state your decision. $Crime~ \hat{per} Student= 33 - 18$ Police per Student $- .35$ Tuition $~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~$ (12) (3) $~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~( .05 )$ =75 =.2134