To be submitted in class on Wednesday (22 July)
Choose from the given options:
1)
A study of class attendance and grades among first year students at a state university
showed that in general students who attended a higher percent of their classes earned
higher grades. Class attendance explained 16% of the variation in grade index among
the students. What is the correlation between attendance and grade index?
a) It could be either 0.4 or -0.4.
b) 0.4.
c) -0.4
d)Not enough information to determine the correlation
2)
2.1)
Which scatter plot has a value of R2 that is closest to 1?
a)Plot 3
b)Plot 2
c)Plot 4
d)Plot 1
2.2)
Which scatter plot has a value of R2 that is close to 0?
a) Not in this list
b) Only Plot 4
c) Both Plots 2 and 3
d) Both Plots 1 and 4
2.3)
Which scatter plot has a negative value for the slope of the least squares regression line?
a) Plot 1
b) Plot 3
c) Plot 2
d) Plot 4
2.4)
Which scatter plot indicates a non-linear relation between the variables?
a)Plot 2
b)Plot 4
c) Plot 3
d) Plot 1
3)
The data below was obtained in a study of number of hours spent by a salesman in a day
(x) versus the number of cars sold (y) by the salesman.
x
y
1
1
2
1
3
2
4
2
5
5
3.1)
The correlation coefficient r between X and Y is close to
a) 0.87
b)0.09
c)0.93
d) None in the list
e)-0.87
3.2)
a)The estimated coefficients of regression line (y = β0 + β1x) are:
b) b0 = 4.90,
and
b1 = 0.10
c)b0 = -0.50,
and
b1 = -0.90
d)b0 = 0.90,
and
e) b0 = -0.50,
b1 = -0.50
and
b1 = 0.90
3.3)
If the number of hours spent is 5, what is the predicted sales
a) y = 2.00
b) y = 1.00
c) y = 4.00
d) y = -5.00
3.5)
Consider the observed data: number of hours spent is 5, and number of cars sold is 5. What
is the residual of this observation:
a) e = 4.00
b) e = 1.00
c) e = -5.00
d) e = 2.00
4)
The mean height of American women is about 65.8 inches and the standard deviation is
about 2.4 inches. The mean height of American men is about 69.2 inches with a standard
deviation of 3.4 inches. The correlation between the heights of husbands and wives is about
0.5. Suppose we transform the data to centimeters, instead of inches (1 inch is
approximately 2.3 cms) Then which of the following statements are correct
A. correlation will remain the same for both the original data and the transformed data
B. The slope of the regression line will remain the same for both sets
C. The intercept of the regression line will remain the same for both sets
a) A and C
b) A and B
c) B and C
d) None of them
e) A, B and C
1)
2)
5)
Pages Price
(H)1
104
32.95
(H)2
188
24.95
(H)3
220
49.5
(H)4
264
79.95
(P)5
336
4.50
(H)6
342
49.95
(P)7
378
4.95
(P)8
385
5.99
(P)9
417
4.95
(H)10 417
39.95
(P)11 436
5.95
(H)12 458
60.00
(H)13 466
49.95
(P)14 469
5.99
(P)15 585
5.95
5.1)
The table gives the number of pages in a book and its price.
The correlation for the above data set is -0.312. What would this lead you to conclude
a) This is possibly a false correlation. It goes against common sense.
b) The price of a book tends to increase as the number of pages increase
c) The price of a book tends to decrease as the number of pages increase
5.2)
Make a rough scatter plot of the above data. What would you now conclude
a) It confirms that the negative correlation is meaningful and price tends to decrease with
number of pages.
b) This correlation is false. There is a lurking variable (possibly hard cover and
soft cover) which distorts the correlation. In each subgroup the price tends to
increase with number of pages.
c) It suggests that a mistake was made in computing correlation.
d) It confirms that the negative correlation is meaningful. There are two subgroups and in
each subgroup price tends to decrease with number of pages.
6)
In a population of couples the average height of wives' was 65.2 inches and that of the
husbands 69 inches. You use the regression line to make predictions of the wife's height
from the husband's height. Suppose a husband has height 69 inches, what would be the
predicted height of the wife?
a) 69
b) Not enough information to answer the question."
c) 65.2
7)
A regression line of the score of Exam 3 on Exam 2 for a 300 level stat course in fall of 2003
yieled the regression line y=3 + 0.71 x. A similar line for a 400 level stat course in fall 2004
yielded y=3 + 0.63 x.
7.1)
Which of the following is true?
a) There is not enough information to draw any conclusions about the correlation.
b) Correlation between the two exams for the 400 level courses is larger than that for the
300 level course.
c) Correlation between the two exams for the 300 level courses is larger than that for the
400 level course.
7.2)
Since the number of students could be different and the standard deviations could be
different the investigator decided to standardize the scores. That is instead of the actual
score in a exam for a student he used the corresponding z-score. This was done for all the
scores in all the exams resulting in the lines
for the 300 level : y= 0+0.77 x
for the 400 level : y= 0+0.57 x
a)Correlation between the two exams for the 400 level courses is larger than that for the
300 level course.
b)Correlation between the two exams for the 300 level courses is larger than that
for the 400 level course.
c) There is not enough information to draw any conclusions about the correlation.
8)
The mean height of American women is about 66 inches and the standard deviation is about
2.4 inches. The mean height of American men is about 69.2 inches with a standard
deviation of 4 inches. The correlation between the heights of husbands and wives is about
0.5. We want to predict the height of the husband whose wife is 68 inches tall.
8.1)
The slope of the appropriate regression line is
a) 45.2400
b) 0.8333
c) 0.3000
d) 14.2022
8.2)
The intercept of the appropriate regression line is
a)0.8333
b) 0.3000
c)45.2400
d)14.2022
8.3)
The predicted value of husbands height when wife's height is 68 inches is
a) 70.8666
b) 68.8333
c)966.5829
8.4)
There are two data points, x1= wife's height=65 with husband's height= 71.7667, and
another pair with x2=68.4 and y2=77.99992. If you use the regression line computed
earlier then
a) The residual at x2 is smaller than the residual at x1
b) The residual at x2 is equalto the residual at x1
c) The residual at x2 is larger than the residual at x1
8.5)
The regression line that you found out in this problem is
b) It does not matter both are the same
c) The regression line of womens's heights on men's heights
d) The regression line of mens's heights on women's heights
9)
9.1)
The blue shaded region represents "A and B" in which figure?
a)Figure 3
b)Figure 1
c)Figure 2
d)Figure 4
9.2)
The blue shaded region represents "A or B" in which figure?
a)Figure 1
b) Figure 3
c) Figure 2
d) Figure 4
9.3)
The blue shaded region represents "only A not B" in which figure?
a)Figure 2
b)Figure 4
c) Figure 1
d) Figure 3
9.4)
The blue shaded region represents "only B not A" in which figure?
a) Figure 3
b) Figure 4
c) Figure 1
d) Figure 2
10)
Suppose the following information are given:
and B) = 0.18.
P(A) = 0.4,
P(B) = 0.38,
P(A
10.1)
Find the probability of the yellow shaded region in Figure 1:
a) 0.38
b) 0.62
c) 0.78
d) 0.2
10.2)
Find the probability of the yellow shaded region in Figure 2:
a)0.62
b)0.6
c) 0.2
d) 0.02
10.3)
Find the probability of the yellow shaded region in Figure 3:
a)1.22
b)0.6
c)0.4
d) 0.22
10.4 )
Find the probability of the yellow shaded region in Figure 4:
a)0.152
b) 0.78
c) 0.42
d) 0.6