Question

The logit model cannot be estimated with Excel. Seton Hall University is a Roman Catholic university situated in New Jersey, with easy access to New York City. Like most universities, it uses SAT scores and high school GPA as primary criteria for admission. The accompanying table shows a portion of data concerning information on admission (Admission equals 1 if admitted, O otherwise), SAT score, and GPA for 30 students who had recently applied to Seton Hall. Admission SATGPA 1,700 3.39 1 2,820 2.65 1 e 1,30e 2.47 Click here for the Excel Data File a-1. Estimate the logit probability model where admission is a function of the SAT score and high school GPA. (Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.) Coefficient Intercept SAT GPA a-2 Analyze the significance of the variables at the 5% level. O The variables are individually significant at the 5% level. O The variables are not individually significant at the 5% level. b. Predict the probability of admission for an individual with a GPA of 3.5 and an SAT score of 1700. (Round coefficient estimates to at least 4 decimal places and final answer to 2 decimal places.) c. Predict the probability of admission for an individual with a GPA of 3.5 and an SAT score of 1800. (Round coefficient estimates to at least 4 decimal places and final answer to 2 decimal places.) Admit | SAT | GPA 1700 3.39 2.65 2230 2.74 3.84 2220 3.02 2.66 1560 2.28 2.28 3.89 3.75 2.81 3.84 4.00 3.37 3.69 3.92 2.89 1750 2.94 2.54 3.30 2.69 2.91 3.56 21002.92 2.98 3.36 3.87 3.76 2.33 2.47 2020 1280 2220 1950 1720 1980 1290 1380 2160 1770 1420 1290 1980 01610 1990 1350 1840 2200 1800 1880 1880 1560 0

Answer 1

View(ad) ad Admit SAT GPA 1 1700 3.39 1 2020 2.65 1 2230 2.74 1 1280 3.84 1 2220 3.02 1 2220 2.66 0 1560 2.28 1 2250 2.28 1 1950 3.89 0 1720 3.75 0 1980 2. 81 1 1290 3.84 1 1380 4.00 1 2160 3. 37 1 1770 3.69 0 1420 3.92 0 1290 2.89 0 1750 2.94 1 1980 2. 54 0 1610 2.30 1 1990 2.69 0 1350 2.91 1 1840 3. 56 1 2100 2.92 1 2200 2.98 1 1800 3. 36 1 1880 3. 87 1 1880 3.76 0 1560 2. 33 0 1300 2.47 10 12 13 14 15 16 17 18 19 21 23 25 26 27 28 29 30

ad <-read.csv("C:/Users/pcc/Desktop/ad.csv") View(ad) Ad ##Logistic model ## l=glm(Admit~SAT+GPA.family = binomíal.data= ad) Output Call: glm(formula- Admit- SAT + GPA, family binomial, data-ad) Coefficients: Intercept) SAT GPA -19.525152 0.006463 2.872288 Degrees of Freedom: 29 Total (i.e. Null)27Residual Null Deviance Residual Deviance: 21.08 AIC: 27.08 38.19 Call: glm(formula- Admit SAT+GPA, family- binomial, data- ad) Deviance Residuals: Min 1Q Median 3Q Max 2 2146-0.3291 0.2643 0.6031 1.2735 Coefficients: Estimate Std. Error z value PrIz) (Intercept) -19.525152 7.748108 -2.520 0.01174* SAT 0.006463 0.002430 2659 0.00783 ** GPA2.872288 1.324255 21600.03008 * Signif codes: 0 ***0.001**0.01 0.05'. 0.11 (Dispersion parameter for binomial family taken to be 1)

Null deviance: 38101on 29 degrees of freedom Residual deviance: 21.alton 27 degrees of freedom AIC: 27.077 ##Here SAT Variable is Significance at 0.001 i.e. Dvalue And GPA is Significant at 0.01 ie p value 0.03008 .00783

B-Probability of admission for an individual with GPA 3.5 & SAT score 1700 newdatal-data frame(SAT-1700, GPA 3.7) predict(l,newdatal,type-response) 0.8197666 Probability of admission for an individual with GPA 3.5 & SAT score 1700 is 0.8197666 C-Probability of admission for an individual with GPA 3.5 & SAT score 1800 is newdata2-data.frame(SAT 1800,GPA 3.5) predict(lnewdata2,type response) 0.8966974 Probability of admission for an individual with GPA 3.5 & SAT score 1800 is 0.8966974