A negative correlation coefficient means that large values of Y occur with small

Question

A negative correlation coefficient means that large values of Y occur with small values of X and small values of Y occur with large values of X. True False If the regression slope coefficient is negative, we know that the explained sum of squares for regression (numerator sum of squares or SSR) will be negative also. True False The proportion of the variation in the dependent variable, which can be explained by its linear relationship with the independent variable, is called the coefficient of determination. True False Relatively large values of a calculated chi-square statistic provide support for the alternate hypothesis in goodness-of-fit tests. True False The ordinal measurement scale required for the application of many nonparametric tests means that a rank must be implicit in the data. True False In a chi-square goodness of fit test with degrees of freedom greater than 1.0, at least 80 percent of the cells should have expected frequencies greater than 5.0. The slope coefficient in a simple regression equation and the correlation coefficient between the same two variables must have the same algebraic sign. True False The regression slope coefficient estimates the change in the dependent variable for each unit change in a particular independent (explanatory) variable when all other independent variables do not change. True False If the R2 value for a regression model is 0.56, the adjusted R2 will be smaller to account for degrees of freedom lost due to additional independent variables in the model. True If the sign on a regression coefficient is negative, this implies that this variable is actually detracting from the explanation of the variation in the dependent variable. True False Multicollinearity refers to the problems that can occur when two or more explanatory variables are correlated among themselves. True False If a particular qualitative variable has 5 categories or response possibilities, the appropriate number of dummy variables to create is five. R2 will sometimes decrease when independent variables are added to the model. True False A valid multiple regression model could be developed if the sample size is ten and the number of independent variables is 15. True False The trend component in a time series is the long-term increase or decrease in the variable. True A Magazine publisher prints 3 different types of magazines. He is interested in seeing whether sales of the different types of magazines are independent of the region in which customers live. A random sample of 700 customers revealed the following table. Enough information is given to complete the table from the four cells. How many customers in the sample were from Region 2 and purchased an entertainment magazine? 80 185 30 Refer to the previous problem. Under the null hypothesis of independence, how many customers should the publisher expect to be from Region 1 and have purchased a news magazine? 60 11.67 0.01 69.11 Refer to the previous problem. To determine whether the type of magazine purchase depends upon region, how many degrees of freedom should be used? 9 6 8 4 Refer to the previous problem. The observed X2 statistic for this problem is 10.011. What is the corresponding p-value? Be as specific as the tables will allow. less than 0.02 greater than 0.10 between 0.05 and 0.10 between 0.02 and 0.05 The editors of a national automotive magazine recently studied 30 different automobiles sold in the United States with the intent of seeing whether they could develop a multiple regression model to explain the variation in highway mileage per gallon. A number of different independent variables were collected. The following correlation matrix was developed: If only one variable were to be brought into the model, which variable should it be if the goal is to explain the highest possible percentage of variation in the dependent variable? displacement curb weight horsepower 0 to 60mph Refer to the previous question. Suppose a model included Curb Weight and Cylinders as independent variables in a regression to explain the variation in highway mileage per gallon, and the inclusion of another independent variable is being considered. The inclusion of which additional variable would pose the least problem when considering the effect of multicollinearity? Displacement Price as Tested 0 to 60 mph Torque Horsepower The ABC Appliance Store is interested in knowing if there is a relationship between the model of washer purchased and the purchaser's credit card balance. Do customers with larger credit balances tend to purchase the higher end models, the lower end models, or is there no relationship between the two variables? Data analysis is presented below.

Explanation / Answer

1. True - A negative correlation implies that as x increases, y decreases.

2. False - The sums of squares (SSR, SSE and SST) must always be positive.

3. True - R^2 = coefficient of determination = % of variation in y = DV explained by the x's = IV's.

4. True - The larger the X^2 test statistic is, the more evidence we have against Ho and in favor of Ha.

5. True - Ordinal data has order, e.g. Exellent, Very Good, Good, Poor, Very Poor.

6. True - But, check your book. This assumption varies from author-to-author. Some suggest that ALL of the expected counts are at least 5 (ie 5 or more).

7. True - For SLR, b1 and r must have the same sign.

8. True - bi tells us... As xi increases by 1 unit, y is predicted in increase/decrease by bi holding all the other predictors constant.

9. True (?) - This may be true depending on your professor / book. Most books say R^2 Adj < R^2 to account for the number of predictors and sample size.

10. False - A variable will NEVER detract from explaining y.

11. True

12. False - # of dummy variables = 5-1 = 4.

13. False - R^2 will NEVER decrease as predictor are added.

14. False - The sample size must be MANY times more than the number of predictors.

15. True

16.

215-60-93 = 62
185-93-62 = 30
Answer: 30

17. Expected = 215 x 225 / 700 = 69.11

18. df = (3-1)(3-1) = 2x2 = 4

19. D - p-value is between .02 and .05

(No question #20)

21. B - Curb weight <-- largest |r|

22. B - Price as Tested <-- smallest |r| with curb Weight and Cylinders

23.

Expected = 74x80/204 = 29.0196

Answer: (16-29.0196)^2/29.0196 = 5.841

24. Model and Balance are independent

25. 16.81 <-- go across from df = (3-1)(4-1) = 6 and down from .01

26. a=7, b=10, c=8, d=12, e=5.5, f=11, g=8.5, h=2, i=4, j=5.5, k=3, l=1

27.

SSR = R^2*SST
SSR = .7560*2659320 = 2010445.92
MSR = SSR/3 = 2010445.92/3 = 670148.64

SSE = SST-SSR
SSE = 2659320-2010445.92 = 648874.08
MSE = 648874.08/26 = 24956.695

F = MSR/MSE = 670148.64/24956.695 = 26.85

28. With each additional block an apartment is away from campus, its monthly rent is predicted to decrease by $10.06 holding the other predictors constant.

29. t = -10.06/4.92 = -2.0447

30. yhat = 14.12 - 10.06(6) + 110.25(4) + 85.21(1) = $479.97

31. D - p-value = .0001 < alpha = .05 --> significant

32. Ho: beta1 = beta2 = beta3 = beta4 = 0

33.

Age: p-value = .00001 < .05 --> Age is useful
D1: p-value = .00001 < .05 --> D1 is useful
D2: p-value = .36770 > .05 --> D2 is NOT useful

34.

Ho: beta2 = 0
t = 4.279
t-critical = 2.750

35. b3 = 46.15

36.

Ho: beta3 = 0
t = 6.622
p-value = .00001 < .01 --> difference is significant

37.

Since Machine C was left out of the equation, the coefficients are relative to Machine C. The positive coefficient for D1 indicates that Machine A runs LONGER before breaking down than Machine C. Similarly, since the coefficient for D2 is negative, it indicates that Machine B breaks down SOONER than Machine C. BUT, the coefficient for D2 is greater than .05, indicating that the run times between Machine B and C are NOT significantly different. Machine's B and C are the least reliable since this there run times are NOT significantly different.

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