____ 1. The closer the points on a scatter diagram fall to the regression line, the _________ between the scores.a. higher the correlationb. lower the correlationc. correlation doesn’t changed. need more information___ 2. The strongest correlation shown below is _________.a. 0.75b. -0.33c. -0.25d. 0.15____ 3. When deciding which measure of correlation to employ with a specific set of data, you should consider _________.a. whether the relationship is linear or nonlinearb. type of scale of measurement for each variablec. a and bd. none of the above____ 4. Which of the following statements concerning Pearson r is not true?a. r = 0.00 represents the absence of a relationship.b. The relationship between the two variables must be nonlinear.c. r = 0.76 has the same predictive power as r = -0.76.d. r = 1.00 represents a perfect relationship.e. All of the above are true statements.____ 5. Spearmans Rho is used _________.a. when both variables are dichotomousb. when both variables are of interval or ratio scalingc. when one or both variables are only of ordinal scalingd. when the data is nonlinear____ 6. When a correlation exists, lowering the range of either of the variables will _________.a. raise the correlationb. lower the correlationc. not change the correlationd. produce a causal relationship____ 7. If two variables are ratio scaled and the relationship is linear, what type of correlation coefficient is most appropriate?a. Pearsonb. Spearmanc. etad. phi____ 8. You have conducted a brilliant study which correlates IQ score with income and find a value of r = 0.75. At the end of the study you find out all the IQ scores were scored 10 points too high. What will the value of r be with the corrected data?a. r will be increasedb. r will be decreasedc. r will remain the samed. cannot be determined____ 9. If 49% of the total variability of Y is accounted for by X, what is the value of r?a. 0.49b. 0.51c. 0.70d. 0.30____ 10. Satisfying the assumption of homoscedasticity allows you to _________.a. Interpret the standard error of estimate b. Calculate multiple Rc. Calculate a standardized regression coefficientd. Decide who has been naughty or niceProblem 1(25 points) We want to examine what factors account for differences in salary in a university department by characteristics of the faculty member. The number of years since each faculty member received his Ph.D. (X1), the number of publications (X2), gender of the professor (1=F, 0=M), and number of citations in the scientific literature (X4).CASE TIME PUBS CITS SALARY FEMALE1 3 18 50 51876 12 6 3 26 54511 13 3 2 50 53425 14 8 17 34 61863 05 9 11 41 52926 16 6 6 37 47034 07 16 38 48 66432 08 10 48 56 61100 09 2 9 19 41934 010 5 22 29 47454 011 5 30 28 49832 112 6 21 31 47047 013 7 10 25 39115 114 11 27 40 59677 015 18 37 61 61458 016 6 8 32 54528 017 9 13 36 60327 118 7 6 69 56600 019 7 12 47 52542 120 3 29 29 50455 121 7 29 35 51647 122 5 7 35 62895 023 7 6 18 53740 024 13 69 90 75822 025 5 11 60 56596 026 8 9 30 55682 127 8 20 27 62091 128 7 41 35 42162 129 2 3 14 52646 130 13 27 56 74199 031 5 14 50 50729 032 3 23 25 70011 033 1 1 35 37939 034 3 7 1 39652 035 9 19 69 68987 036 3 11 69 55579 037 9 31 27 54671 038 3 9 50 57704 039 4 12 32 44045 140 10 32 33 51122 041 1 26 45 47082 042 11 12 54 60009 043 5 9 47 58632 044 1 6 29 38340 045 21 39 69 71219 046 7 16 47 53712 147 5 12 43 54782 148 16 50 55 83503 049 5 18 33 47212 050 4 16 28 52840 151 5 5 42 53650 052 11 20 24 50931 053 16 50 31 66784 154 3 6 27 49751 155 4 19 83 74343 156 4 11 49 57710 157 5 13 14 52676 058 6 3 36 41195 159 4 8 34 45662 160 8 11 70 47606 161 3 25 27 44301 162 4 4 28 58582 1What percent of the total variance is accounted for by all four predictor variables after correcting for attenuation._____Insert a number that reflects the error in prediction? _________Insert the complete regression line below.For each unit change in Number of publications how much does salary change and in what direction?__ ___For each unit change in Number of citations how much does salary change and in what direction?___ ____For each unit change in Years since the PhD how much does salary change and in what direction?___ ____For each unit change in Gender how much does salary change and in what direction?___ ____For each standard deviation change in Number of publications how much does salary change and in what direction?____ ___For each standard deviation change Number of citations how much does salary change and in what direction?______For each standard deviation change in Years since the PhD how much does salary change and in what direction?_______For each standard deviation change in Gender how much does salary change and in what direction?______What percent of the variance in salary is uniquely accounted for by Number of publications?______What percent of the variance in salary is uniquely accounted for by Number of Citations?_______What percent of the variance in salary is uniquely accounted for by Years since the PHd? _______What percent of the variance in salary is uniquely accounted for by Sex?____What number is in the denominator of the t-test that is testing the significance of the variance uniquely accounted for by Number of publications?____What number is in the denominator of the t-test that is testing the significance of the variance uniquely accounted for by Number of Citations?____What number is in the denominator of the t-test that is testing the significance of the variance uniquely accounted for by Years since the PHd?____What number is in the denominator of the t-test that is testing the significance of the variance uniquely accounted for by Sex?____Which predictor variable has the strongest relationship with salary and how do you know this?Is there a problem with multicollinearity?How do you know.Problem 2(15 points) The state of Vermont is divided into 10 health planning districts- they correspond roughly to counties. The following data represent the percentage of live births of babies weighing under 2500 grams (Y), total high-risk fertility rate for females 17 years of age or younger (X1), total high-risk fertility rate for females younger than 17 years of age or older than 35 years of age (X2), percentage of mothers with fewer than 12 years of education (X3), percentage of births to unmarried mothers (X4), and percentage of mothers not seeking medical care until the third trimester (X5).Calculate a multiple regression using X1 to X5 as predictors and Y as the dependent variable. Compute a simultaneous multiple regression on the data posted below.Y X1 X2 X3 X4 X56.10 22.80 43.00 23.80 9.20 6.007.10 28.70 55.30 24.80 12.00 10.007.40 29.70 48.50 23.90 10.40 5.006.30 18.30 38.80 16.60 9.80 4.006.50 21.10 46.20 19.60 9.80 5.005.70 21.20 39.90 21.40 7.70 6.006.60 22.20 43.10 20.70 10.90 7.008.10 22.30 48.50 21.80 9.50 5.006.30 21.80 40.00 20.60 11.60 7.006.90 31.20 56.70 25.20 11.60 9.001).Use the output to answer the following questions.(1) With all five variables in the model what percent of the variance is accounted for aftere correcting for inflation? (1) For model 1 with all 5 predictor variables in the equation, what is the standard error of estimate? (2) From the printout what numbers make the t ratio for testing the significance of X4? (2) With all five variables in the model, for each unit change in X1 what happens to Y and by how much. (2) With all five variables in the model, for each standard deviation change in X3 how much of a standard deviation change in Y occurs and in what direction. (2) What percent of the variance in Y is uniquely accounts for by X2 (1) What percent of the variance in Y is uniquely accounted for by X5 (that is accounted for by X5 after X1, X2, X3, X4 are accounted for). (1) The null hypothesis that is tested when using regression coefficients is what? (2) A correlation between predictor variables of .8 or above increases the chance of colinearity problems. Which if any predictor variables are a risk for problems with collinearity?