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# Correlation and Regression Review

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5

Answer questions 5-8 using the following information:
Test the hypothesis that the treatment means for samples given below are equal. Use the .01 significance level.
Treatment 1 Treatment 2 Treatment 3
22 34 13
20 31 10
21 25 14
18 25 11
19 32
30

The decision rule is:
a. Reject the null hypothesis if F > 5.42
b. Reject the null hypothesis if F > 6.93
c. Accept the null hypothesis if F > 26.9
d. Reject the null hypothesis if F > 99.4

6

SS total is:
a. -4,132.8
b. 755.83
c. 845.33
d. 4,132.8.

7

MSE is:
a. 7.46
b. 377.92
c. 422.66
d. 2,066.4

8

The F statistic =
a. 1.00
b. 7.46
c. 50.67
d. 54.5

9

Based on the analysis of variance we would fail to reject Ho.
a. True
b. False

10

In an experiment in which two of four similar units are each compressed at three different levels (light, medium, heavy) to determine resilience, the number of degrees of freedom (numerator, denominator) is:
a. (2,3)
b. (2,6)
c. (1,4)
d. (1,3)

11

The following data apply to a two-factor ANOVA:
Treatment
Source 1 2 3
A 12 14 8
B 9 11 9
C 7 8 8

SST for the data =
a. 1.36
b. 10.89
c. 31.11
d. 42.22

12

SSB for the data =
a. 20.22
b. 31.11
c. 53.33
d. 63.11

13

The regression equation:
a. can be adjusted to accommodate any number of independent variables.
b. indicates an inverse relationship between variables when a "b" coefficient has a negative sign.
c. should only be used to predict values for the dependent variable that are inside the range of the sample values.
d. both a and b.
e. all of the above.

14

The measure of explained variation is the:
a. coefficient of multiple determination.
b. coefficient of multiple nondetermination.
c. regression coefficient.
d. correlation matrix.

15

An analyst determines the relationship between the time taken to perform a computer-triggered production function (Y), required memory to run the function (000 bytes) and amount of input (000 lines of data). The regression equation representing this relationship is determined to be:
Y'=11.43 + 1.26X1 + 3.11X2
For required memory of 25,000 bytes of data, and input of 8,000 lines of data, the estimated time to run the function is:
a. 14.233 minutes
b. 67.81 minutes
c. 73.69 minutes
d. 129.43 minutes
e. not calculable without additional data.

16

For a run that required a memory of 15,000 bytes and input of 8,000 lines the time of the run is 54 minutes; this is:
a. 13 minutes less than expected.
b. 1.2 minutes less than expected.
c. 1.2 minutes more than expected.
d. not calculable without additional data.

17

Correlation analysis:
a. measures the extent to which changes in an independent variable cause changes in a dependent variable.
b. refers to a group of techniques to measure the strength of the association between two variables.
c. measures relationships in terms of strong (a positive r value); moderate (an r value close to zero); and weak (a negative r value).
d. is the development of a mathematical model to estimate the value of one variable based on the value of another.
e. both b and d.
f. all of the above.

18
Marks: 1
An r value of -0.75 indicates:
a. weak negative correlation between variables.
b. weak positive correlation between variables.
c. strong negative correlation between variables.
d. virtually no correlation between variables.

19
Marks: 1
x 2 4 1 5 3
y 15 25 10 40 30

&#931;(X2) =
a. 55
b. 3,025
c. 3,450
d. 14,400

20

&#931;(Y2) =
a. 225
b. 3,450
c. 6,800
d. 14,400

21

r =
a. -0.0025
b. 0.073
c. 0.927
d. 1.08

22

The r value indicates:
a. moderately weak negative correlation between x and y.
b. moderately strong negative correlation between x and y.
c. weak positive correlation between x and y.
d. strong correlation between x and y.

23

The percentage of variation in a dependent variable that is explained by an independent variable is known as the:
a. correlation of the variables.
b. coefficient of correlation.
c. coefficient of determination.
d. regression equation.

24

For the data presented for questions 19-22, the proportion of total variation in y that is explained by x is:
a. 7%
b. 14%
c. 74%
d. 86%

25

The coefficient of determination:
a. must be a positive number.
b. cannot be larger, in absolute terms, than the coefficient of correlation.
c. must be greater, in absolute terms, than the coefficient of nondetermination.
d. is negative when the coefficient of nondetermination is negative.
e. both a and b.
f. all of the above.

26

A sample of 25 shipments of a product from a warehouse indicates that the correlation between number of defects and processing speed is 0.56. At the .05 significance level,:
a. t = 1.714, indicating no positive association between the two variables.
b. t = -1.94, indicating a negative association between the two variables.
c. t = 1.94, indicating a positive association between the two variables.
d. t = 3.24, indicating a positive association between the two variables.

27

The least-squares regression equation:
a. is determined by minimizing total squared error between the actual Y values and the predicted values of Y.
b. is used to estimate the value of the dependent variable Y based on any value for the independent variable X.
c. determines the amount of correlation between the X and Y variables.
d. is determined by minimizing the total error between the X and Y values.
e. both a and c.
f. both b and d.

28

In the linear regression equation Y = a + bx, the slope is represented by:
a. a
b. b
c. x
d. y

29

x 2 4 6 8 10
y 3 1 7 5 9

The value of b is:
a. 0.8
b. 1.0
c. 2.2
d. 4.0

30

For this data, a value of 5 for x would yield a predicted value for y of:
a. 1.24
b. 4.20
c. 6
d. 12

31
The correlation coefficient (r) for this data is :
a. -0.2
b. 0.64
c. 0.80
d. 0.89
e. none of the above.

32

The overall accuracy of a regression procedure may be estimated by the degree of scatter about the regression line provided the sample results.
a. True
b. False

33

For the data given for questions 29-31, the standard error of the estimate is:
a. 1.27
b. 2.19
c. 3.45
d. not calculable without additional data.

34

The application of linear regression is based on the assumption that:
a. for each x value, there is a group of Y values that is normally distributed.
b. the means of the normal distributions of Y values all lie on the straight line of regression.
c. the standard deviations of the Y values are equal.
d. Y values are statistically independent.
e. both a and b.
f. all of the above.

35

For the data given for questions 29-31, a 95% confidence interval for Y' for an x value of 9 is:
a. [3.59, 10.81]
b. [2.86, 11.94]
c. [5.34, 9.42]
d. [5.05 ,9.74]
e. [4.53, 13.47]

36

A confidence interval:
a. refers to a particular case for a given value of X.
b. determines a particular value for Y given a certain X value.
c. determines the mean value of Y for a given X.
d. increases in size as the level of confidence decreases.
e. both b and d.
f. all of the above.

37
r2 measures the reduction in the total sum of squares achieved by fitting the regression line.
a. True
b. False

38

Total explained variation for the data presented in questions 29-31 is:
a. 14.4
b. 11.2
c. 17.4
d. 25.6
e. 40

39

Source DF SS MS
Regression 1 7,582 ---
Error 29 524.5 ---
Total 30 --- ---

Total variation is:
a. 7,057.50
b. 7,582
c. 8,106.50
d. not calculable without additional data.

40

The coefficient of determination is
a. 0.874
b. 0.935
c. 0.967
d. 1.074

41

The standard error of the estimate is:
a. 4.253
b. 16.17
c. 18.09
d. 419