Deck 19: Correlation Analysis and Regression Analysis

Question 1

r² is the square of the correlation between X and Y and also the ^ square of the correlation between Y and Y.

Answer 1

True

Question 2

A regression model can accurately predict the level of a dependent variable in a changing market environment.

Answer 2

False

Question 3

An independent variable which takes a small number 3 or 4) of discrete values is often termed a dummy variable.

Answer 3

False

Question 4

The total variation in Y, the dependent variable, can be expressed as the sum of the explained variance, the unexplained variance, and an unknown error.

Question 5

The unexplained variation in Y is estimated by n ^ $\Sigma$ Y_i - Y₁)² i=1

Question 6

A regression model can be used to accurately predict the level of a dependent variable, given extreme values of an independent variable.

Question 7

The larger the beta coefficient value, the stronger the effect of that variable upon the dependent variable.

Question 8

The model: Y = $\alpha$ + $\beta$ X² + e hypothesizes a curvilinear relationship between X and Y.

Question 9

The sole purpose of regression analysis is to predict the level of a dependent variable, given proposed levels of the independent variables.

Question 10

Regression is an analysis of dependence technique since it involves a dependent variable as the focus of analysis.

Question 11

If the standard deviation of X is approximated by s, then the standard deviation of the mean based on a sample size of n) is s/F $\surd$ n.

Question 12

When an understanding of the relationship between X and Y is the motivation behind data analysis, the estimate of the $\beta$ parameter is of primary importance.

Question 13

A least squares criterion minimizes the squared vertical deviations from the regression line.

Question 14

If a variable that is excluded from the model is correlated with an independent variable in the model, the regression coefficient will reflect the impact of the excluded variable on the dependent variable.

Question 15

In interpreting parameter coefficients, $\beta$ indicates that if the independent variable X is changed by one unit, the dependent variable Y will change by $\beta$ units.In multiple regression, we add the constraint that the values of all other independent variables remain constant.

Question 16

When testing the hypothesis that, in fact, $\beta$ = 0, the researcher is actually testing the hypothesis that the independent variable has no linear) effect on the dependent variable.

Question 17

r² = Total variation - Unexplained variation Total variation

Question 18

If the parameter $\beta$ is zero, the value of must also always be zero.F

Question 19

In regression analysis, the dependent variable is sometimes called the predictor variable.

Question 20

Correlation analysis involves measuring the strength of the relationship between two variables.

Question 21

The degree of linear association between two intervally scaled variables is measured by

A)Pearson correlation coefficient
B)significance level
C)analysis of variance
D) $\beta$

Question 22

A confidence coefficient is denoted by the symbol

A) $\alpha$
B)1- $\alpha$
C) $\beta$
D)1- $\beta$

Question 23

Which one of the following is the same as standard deviation of regression coefficient?

A)sum of squares of errors
B)standard error
C)predicted value
D)standard error of the estimate

Question 24

In analysis of variance, if RHO = 0, the explained variance is

A)unexplained
B)unknown
C)total
D)zero
E)one

Question 25

Correlation coefficient implies a causal relationship between variables.

Question 26

In analysis of variance, the hypothesis that the means are equal will be rejected if

A)the total mean square error is significantly greater than either the explained or unexplained mean square error
B)the total mean square error is significantly greater than the unexplained
C)the total mean square error is significantly greater than the explained
D)the mean square error explained is significantly greater than the mean square unexplained
E)the mean square error unexplained is significantly greater than the mean square explained

Question 27

Partial correlation coefficient is the measure of association between two variables controlling for the effect of one or more additional variables.

Question 28

The point estimates b₀ and b₁ in a regression analysis, tend to increase the total sum of squares.

Question 29

The knowledge of the regression coefficient and the t value can suggest the extent of association an independent variable has on the dependent variable.

Question 30

The error term is not normally distributed is an assumption of the regression analysis.

Question 31

Which of the following is not an assumption of the regression model?

A)the error term is normally distributed
B)the error terms are independent of each other
C)the values of independent variable are fixed
D)the independent variable is normally distributed

Question 32

The Pearson correlation coefficient measures the degree to which there is a linear association between two intervally scaled variables.

Question 33

To examine the association between two variables after controlling for the other variables the researcher should use

A)bivariate correlation
B)partial correlation
C)product moment correlation
D)simple correlation

Question 34

Snow Belt Airlines weighed the baggage of 100 passengers and found the mean weight to be 34.2 pounds with a standard deviation of 14 pounds.What is the 95% onfidence interval for the actual weight of the aggage ? Round Z to the nearest whole number)

A)20.0 - 48.2
B)32.8 - 35.6
C)31.4 - 37.0
D)0.0 - 50.0

Question 35

In doing the statistical test in analysis of variance problem, you accept the null hypothesis while testing with n alpha = .01.You were later told that you should have tested the null hypothesis with alpha = .05.You should

A)change nothing since the outcome is the same
B)re-test since the results might change
C)accept the null hypothesis since the result is just the opposite with alpha = .05
D)consider taking a larger sample size to decrease alpha
E)none of the above

Question 36

If you tested a null hypothesis on problem 7, and accepted it, the probability of Type I error would be

A).95
B).50
C).10
D).05
E)zero

Question 37

One of the best ways to analyze relationships between two sets of nominal data is by doing

A)correlations
B)analysis of variance
C)regression analysis
D)contingency tables
E)none of the above

Question 38

The difference between the actual and the predicted values in a regression equation is called residuals.

Question 39

Although the least-squares regression line provides a reasonable fit of the data points, there are some deviations in the sample data about the line.

Question 40

The measures of association represented by r and r² are

A)symmetric
B)dependant
C)asymmetric
D)independent

Question 41

There are ______ degrees of freedom associated with a sample variance

A)n
B)n-1
C)n-2
D)n₁- + n₂ - 2

Question 42

In the simple linear regression model, Y = $\alpha$ + $\beta$ X + e,

A)the errors are assumed to be as likely to occur above the line as below the line.
B)the errors are assumed to be more likely to occur above the line than below it.
C)the errors are assumed to be more likely to occur below the line than above it.
D)it is assumed that the error is larger for larger values of X.
E)it is assumed that the error is smaller for larger values of X.

Question 43

A 95% confidence interval means

A)a researcher is 95% sure of the study results
B)respondents are confident, on the average, of 95% of the answers they give
C)chi-square tests are equal to .95
D)95 out of 100 samples taken from that universe would give results in the interval

Question 44

A two-dimensional graph in which two variables are plotted is called a

A)comparison plot
B)double dimensional plot
C)scatter diagram
D)venn diagram
E)none of the above

Question 45

A term used to characterize the relative flatness or peakedness of a distribution of variable values is

A)skewness
B)kurtosis
C)semi-inter-quartile range
D)dispersion

Question 46

Based on the regression model, ^ ^ If Y = 50 + 25X, where Y = estimated sales level X = advertising 1-the actual sales level, when X = 2, is 100. 2-when X = 3, the estimated sales level is 125. 3-when X = 3, the estimated sales level is 175. 4-when X = 3, the actual sales level is 125.

A)1
B)2
C)3
D)4
E)1 and 4

Question 47

A regression analysis has shown that there is a definite, positive relationship between sales dependent variable.and advertising and sales promotion all units in dollars).The estimated relationship is sales = 3) advertising + 1) sales promotion + 1,500.Based on the given information

A)all marketing resources should be allocated to advertising, if possible.
B)all marketing resources should be allocated to sales promotion, if possible.
C)the allocation between advertising and sales promotion should be split in the ratio 3 to 1 in all circumstances.
D)since both variables exhibit a positive relationship to sales, resources should be allocated equally between sales promotion and
Advertising in all circumstances.
E)none of the above.

Question 48

Data were collected from refrigerator customers on variables relating to purchase frequency, preferences, and demographic characteristics, etc.To aid in marketing strategy formulation, the data were analyzed in various stages.The significant results at each stage were: Stage 1: high correlation between refrigerator ownership and the number of years married. Stage 2: Refrigerator customers were divided into three different groups based on their age, income, and years of education. Stage 3: perceptual mapping of the three groups showed that none of the existing brands was perceived as particularly satisfying by members in group 2. Which of the following sequences of research methods would have helped in giving the results above? Stage 1 Stage 2 Stage 3

A)Analysis of Perceptual Analysis of dependence mapping association
B)Discriminant Correlation Factor analysis analysis analysis
C)Factor Regression Multidimensional analysis analysis scaling
D)Analysis of Analysis of Analysis of association independence dependence
E)Correlation Discriminant Multi-dimensional analysis analysis scaling

Question 49

^ Consider the estimated relationship: Y = 50 + 50X. 1-The average level of Y, if X = 0, is 50. 2-For each unit increase in $\alpha$ , Y will increase by 50 units. 3-For each unit increase in X, Y will increase by 50 units.

A)1
B)2
C)3
D)1 and 2
E)1 and 3

Question 50

Which of the following data analysis techniques can be termed analysis of dependence techniques?

A)Correlation analysis
B)Regression analysis
C)Multidimensional scaling
D)Cluster analysis
E)Factor analysis

Question 51

Consider the following: Based on the above information, which of these statements is not true? ^

A)The estimated model is Y = -40 + 10X₁ - 5X₂ + 40X₃.
B)The t-value for $\beta$ ₂ is -1/3.
C)It can be concluded that X₃, X₁, and X₂ have the greatest impact on Y, in that order.
D)A unit increase in X₂ will result in a decrease of 5 units in the value of Y, when the values of X₁ and X₃ are held constant.
E)All of these are true.

Question 52

Consider the following: Y = 20 + 30X S_b = 20 1-The value of t is 1.0. 2-The value of t is 1.5. 3-The evidence suggests that $\beta$ = 0. 4-The evidence suggests that $\beta$$\neq$ 0.

A)1
B)2
C)3
D)4
E)2 and 4