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Chapter 14 / Exercise 56
Nature of Mathematics
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Why not? What do we look at to answer this question? 11
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Chapter 14 / Exercise 56
Nature of Mathematics
Smith Expert Verified
Thus jar we've found that both "Training" and "Salary" are related to "Performance Rating". How can we capitalize on both of these relationships? By building a multiple regression equation (i.e., using multiple predictor variables in the same equation). Mtb Express: Statistics Multiple Regression Regression Analysis: perform versus training, salary Model Summary s = 5.947 R-Sq = 89.6% R-Sq(adj) = 88.7% Coefficients Predictor coef SE Coef T-value P-value Constant -30.83 10.86 -2.84 0.010 training 3.2569 0.3886 8.38 0.000 salary 0 . 06919 0.01471 4.70 0.000 Regression equation perform= - 30.8 + 3.26 training + 0.0692 salary -3 0 . 8 This is the average performance rating for those whose training= 0 and whose salary= 0. As is often (not always) the case, such data values are outside the range of values used to develop this model, and hence we should not interpret this Y-intercept in this problem context. 3. 26 Average performance increases 3.26 points for each additional day of training, given that the relationship between salary and performance has already been taken into account (or, given that salary is held constant) . . 06 92 Average performance increases .0692 points for each additional dollar of weekly salary, given that the relationship between training and performance has already been taken into account (or, given training held constant). 12
How was it that "training" explained 79% of the variation in performance ratings "salary" explained 56% of the variation in performance ratings But when the data for both predictors was used together, we still were able to explain only 89% of the variation in "performance"? predictor variables are related to each other, as well as to Y + Analysis difficulties created by multicollinearity: ~~usfy, l ll!ilfiMops : ~ :: WiU~bounce atound'l - (~ld even switch sign "' t~ty~~--~&inationof Pl"~ictors in _ the equation " 13 __
+ Using categorical predictor variables in regression: How can we incorporate a nominal-scaled variable as a regression predictor variable? Refer again to the data file USTsurvey.mtw Our "Response variable" is "\$ spent on last date by you" The "Predictor variable" is "Gender" How different are the average date spending amounts for males vs.females? Descriptive Statistics: date\$you Variable gender N N* Mean SE Mean StDev Minimum Q1 date\$you 0 135 9 7.339 0.795 9.235 0.000000000 0 .0 00000000 1 133 7 28.56 2.05 23.60 0.000000000 15.00 * 7 0 6.29 4.20 11.10 0.000000000 0.000000000 Variable gender Median Q3 Maximum date\$you 0 5.000 12.000 50.000 1 20.00 40.00 120.00 * 0.000000000 10.00 30.00 15
. ~- - - What if we use "Gender" as a predictor in a regression equation How do we know our interpretation of the "slope" coefficient needs to change? Regression Analysis: date\$you versus gender s = 17.87 R-Sq = 26 . 2% R-Sq(adj) = 25.9% Predictor Coef SE coef T p Constant 7.339 1.538 4.77 0.000 gender 21.218 2.183 9. 72 0.000 Regression equation date\$you = 7.34 + 21.2 gender How do we interpret the 7.34? How do we interpret the 21.2? We need to "write out the mod e /for each different value of the nominal-scale predictor variable; i.e ..
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