Choose the correct answer with a brief justification: (i) Select the most likely
ID: 3244756 • Letter: C
Question
Choose the correct answer with a brief justification: (i) Select the most likely answer for the correlation coefficient for the two variables described below. X = a college student's weight (in lbs): Y = the student's GPA. (a) r = 0.98: (b) r = 0.65: (c) r = 0.07: (d) r = -0.65 (ii) Suppose we have eight data point which exactly fall on the straight line y = -2x + 3. What value should we get for r? (a) r = 3.0: (b) r = 2.0: (c) r = 1.0: (d) r = -1.0 (iii) Select the most likely value for the correlation coefficient for the two variables described below. X = number of police patrol cars making rounds in a neighborhood in a week. Y = number of burglaries committed in the neighborhood pet week. (a) r = 1.14: (b) r = 0.78: (c) r = -0.13: (d) r = -0.75 (iv) From a bivariate dataset we have the following information: Average of x-values = 20.9, average of y-values = 30.9, standard dev. of x-values = 1.1, standard dev. of y-values = 2.2, correlation coefficient = 0.50. The regression line is: (a) y = 2x + 10: (b) y = x - 10: (c) y = x + 10: (d) 2x - 10. (v) A bivariate dataset is collected on a few individuals where X = monthly income, and Y = money spent on gasoline per month. If everyone stars spending double overnight on gasoline, then it would (a) alter the regression line, but not r: (b) alter r, but not the regression line: (c) alter both the regression line and r: (d) alter neither the regression line, nor r.Explanation / Answer
4)
i) There is almost no relation between a student's weight and his GPA. So it is most likely that r=0.07.
Hence option C.
ii) As we increase the values of X , the values of Y decrease. Also, since all the points lie on the same line, r=-1.
Hence option D.
iii) As the number of burgalaries increase, the number of police cars would also increase. There is a strong correlation between these 2 variables. Hence most likely , r=0.78
Hence option B.
iv) Since the new variables follow an exact relationship, r would not be affected but since the spending is doubled, the regresssion line will be altered.
Hence option A.