menuicon

MATH1015 Quizzes

Quiz 3: Mean, Variance, Correlation and Regression
Question 1 Questions
A set of values, xi, has i=16x i = 40 and i=16x i2 = 1600. What are the sample mean, x¯, and sample variance, s2 ? Exactly one option must be correct)
a)
x¯ = 6.66̇, s2 = 0
b)
x¯ = 6.66̇, s2 = 1333.3̇
c)
x¯ = 6.66̇, s2 = 266.66̇
d)
x¯ = 266.66̇, s2 = 16.32

Choice (a) is incorrect
Choice (b) is incorrect
Choice (c) is correct!
x¯ = 1 6 i=16x i = 40 6 = 6.66̇ s2 = 1 n 1 i=16x i2 1 n i=16x i 2 = 1 5(1600 1 6(40)2) = 266.66̇
Choice (d) is incorrect
Suppose i=17x i = 21 and i=19x i = 24. Find x8 + x9. Exactly one option must be correct)
a)
3
b)
-3
c)
45
d)
There is not enough information provided.

Choice (a) is correct!
x8 + x9 = i=19x i i=17x i = 24 21 = 3.
Choice (b) is incorrect
Choice (c) is incorrect
Choice (d) is incorrect
Consider the following frequency table (i = 1,,4)
 
xi1234 fi3621 Find the mean of this data set. Exactly one option must be correct)
a)
6.25
b)
6
c)
2
d)
2.083̇

Choice (a) is incorrect
Choice (b) is incorrect
Choice (c) is incorrect
Choice (d) is correct!
x¯ = 1 12 i=14fixi.
x¯ = 1 12(3 + 12 + 6 + 4) = 25 12 = 2.083.
The following table gives the relation between pairs of data values (xi,yi) for i = 1,,5.
 
xi1234 5 yi 246810 All the points lie on the line y = bx with slope b and correlation coefficient r. Find b and r. Exactly one option must be correct)
a)
r = 2, b = 1
b)
r = 2, b = 2
c)
r = 1, b = 2
d)
r = 1, b = 1 2

Choice (a) is incorrect
Choice (b) is incorrect
Choice (c) is correct!
The line is clearly y = 2x, so b = 2. Since the relationship is linear and the slope is positive, r = 1.
Choice (d) is incorrect
The correlation coefficient r satisfies
0 r2 1.
Which of the following statements is true ? Exactly one option must be correct)
a)
1 r 1
b)
r 1
c)
r 1
d)
r 1 or r 1

Choice (a) is correct!
In general if x2 < a then a < x < a.
Choice (b) is incorrect
Choice (c) is incorrect
Choice (d) is incorrect
Calculate the correlation coefficient, r, (to 2dp) for the bivariate data (xi,yi) : (0,0)(3,1.4)(6,2.6)(7,3.8)(9,7.2). You may use the totals: ixi2 = 175 and iyi2 = 75. Exactly one option must be correct)
a)
0.93
b)
0.09
c)
0.97
d)
None of these.

Choice (a) is correct!
ixi = 25, iyi = 15, ixiyi = 111.2 so Sxx = 50,Syy = 30 and Sxy = 36.2 and r = 36.2 50×30 = 0.93 to 2dp.
Choice (b) is incorrect
Check your calculations for Sxx, Syy and Sxy.
Choice (c) is incorrect
Check your calculations for Sxx, Syy and Sxy.
Choice (d) is incorrect
Check your calculations for Sxx, Syy and Sxy.
The correlation coefficient for a set of bivariate data (xi,yi) is r = 0.87, where the xi are measured in inches and the yi are measured in lbs. A second analyst records the xi values in cm. (1 inch 2.5 cm). What is the second analyst’s value of the correlation coefficient (to 2dp)? Exactly one option must be correct)
a)
0.35
b)
0.87
c)
2.18
d)
Unable to determine without knowing the yi units.

Choice (a) is incorrect
How do you adjust r for a change of units?
Choice (b) is correct!
r is not affected by a change of units.
Choice (c) is incorrect
r cannot exceed 1.
Choice (d) is incorrect
How do you adjust r for a change of units?
Find the correlation coefficient for 6 pairs of observations if the LSR line is y = 0.5 0.05x and if 81% of the variation in y is explained by regression on x. Exactly one option must be correct)
a)
0.9
b)
0.81
c)
0.05
d)
None of these.

Choice (a) is incorrect
Check the slope of the LSR line.
Choice (b) is incorrect
This is r2.
Choice (c) is incorrect
Try again.
Choice (d) is correct!
The slope is negative and r2 = 0.81, so r = 0.9.
For the bivariate data (x1,y1)(x2,y2)(xn,yn), the least squares regression line is fitted. The line is y = 2.51 4.1x. You know that the first data point is (x1,y1) = (0.1,2.0), so the residual at this point is: Exactly one option must be correct)
a)
2.1
b)
0.1
c)
0.1
d)
2.0

Choice (a) is incorrect
You have found the y value on the LSR line at x = 0.1.
Choice (b) is correct!
At x = 0.1, the value of y on the LSR line is ŷ = 2.51 0.41 = 2.1. Therefore the residual at x = 0.1 is 2.0 2.1 = 0.1.
Choice (c) is incorrect
Try again.
Choice (d) is incorrect
Try again.
A correlation coefficient of r = 0.8 is reported for a sample of pairs (xi,yi). Without any further information, this implies that: Exactly one option must be correct)
a)
as the x values decrease, the y values increase.
b)
80% of the variation in y is due to regression on x.
c)
the (xi,yi) are scattered about a straight line of unknown positive slope.
d)
the (xi,yi) are scattered about a straight line of slope 0.8.

Choice (a) is incorrect
This would be the answer for a negative value of r.
Choice (b) is incorrect
This is the interpretation of r2 not of r.
Choice (c) is correct!
Choice (d) is incorrect
r is not the slope of the LSR line.