Question 1

In correlation analysis, the strength of the association between the variables under investigation is determined by:

Accepted Answer

A)  how close the coefficient is to zero. 
B)  how close the significance value is to 1. 
C)  how close the coefficient is to ±1. 
D)  whether the coefficient is positive or negative.

Question 2

Which of the following is not true for regression?

Accepted Answer

A)  It determines the direction of association. 
B)  It determines the strength of association. 
C)  It predicts value of one variable based on the value of another variable. 
D)  It determines the variance in the direction of the relationship between three or more variables.

Question 3

When examining regression results, how well the model fits the data is determined by consulting the:

Accepted Answer

A)  R-square. 
B)  F statistic. 
C)  standardised coefficient. 
D)  calculated t-value.

Question 4

The regression output for sales and number of salespeople are shown below. Model summary
$$\begin{array} { | l | c | r | r | r | } 
\hline \text { Model } & \boldsymbol { R } & \boldsymbol { R } \text {-square } & \begin{array} { c } 
\text { Adjusted } \
\boldsymbol { R } \text {-square }
\end{array} & \begin{array} { r } 
\text { Std. error of } \
\text { the estimate }
\end{array} \
\hline 1 & .746 ( \mathrm { a } ) & .556 & .541 & 46.873 \
\hline
\end{array}$$ a Predictors: (Constant), number of salespeople
ANOVA(b)
$$\begin{array} { | l | l | r | r | r | r | r | } 
\hline \text { Model } & & \begin{array} { c } 
\text { Sum of } \
\text { Squares }
\end{array} &  { \boldsymbol {d f } } & \text { Mean square } & \boldsymbol { F } & { \text { Sig. } } \
\hline 1 & \text { Regression } & 77152.238 & 1 & 77152.238 & 35.117 & .000 ( \mathrm { a } ) \
\hline & \text { Residual } & 61516.962 & 28 & 2197.034 & & \
\hline & \text { Total } & 138669.200 & 29 & & & \
\hline
\end{array}$$ a Predictors: (Constant), number of salespeople
B Dependent Variable: Sales (A$'000)
Coefficients(a)
$$\begin{array} { | l | l | cr | r | r | r |} 
\hline\text { Model } & &  { \begin{array} { c } 
\text { Unstandardised } \
\text { coefficients }
\end{array} } && \begin{array} { c } 
\text { Standardised } \
\text { coefficients }
\end{array} & { \boldsymbol { t } } & { \text { Sig. } } \
\hline & & \boldsymbol { B } & \text { Std. Error } & \text { Beta } & & \
\hline 1 & \text { (Constant) } & 72.612 & 9.203 & & 2.565 & .013 \
\hline & \text { Number of salespeople } & 35.623 & 3.296 & .201 & 5.926 & .064 \
\hline
\end{array}$$ a Dependent variable: Sales (A$'000)
The above shows that for every one-unit increase in number of salespeople, average sales will increase by approximately:

Accepted Answer

A)  36 units. 
B)  73 units. 
C)  75 units. 
D)  108 units.

Question 5

The mathematical symbol Y is commonly used for the independent variable, and X typically denotes the dependent variable.

Accepted Answer

A) True 
 B)False

Question 6

The coefficient of determination, r², ranges from:

Accepted Answer

A)  zero to +1.0. 
B)  -1.0 to zero. 
C)  -1.0 to +1.0. 
D)  -2.0 to +2.0.

Question 7

To use the Chi-square test, both variables in a 2 x 2 contingency table must be measured on a ratio or interval scale.

Accepted Answer

A) True 
 B)False

Question 8

A correlation matrix can quickly give the researcher an overview of the direction, strength and statistical significance of each paired relationship.

Accepted Answer

A) True 
 B)False

Question 9

To compute the Chi-square value for the contingency table, the researcher must first identify an expected distribution for that table.

Accepted Answer

A) True 
 B)False

Question 10

In correlation analysis, if associated values of the two variables differ from their means in the same direction, their covariance will be negative.

Accepted Answer

A) True 
 B)False

Question 11

A Spearman's rank-order correlation coefficient examines the relationship between two ordinal variables.

Accepted Answer

A) True 
 B)False

Question 12

The correlations table below indicates that: Correlations
$\begin{array}{|l|l|r|r|}
\hline & & {\text { Sales }} & \begin{array}{r}
\text { Advertising } \
\text { expenditure }
\end{array} \
\hline \text { Sales } & \text { Pearson correlation } & 1 & 0.753 (^{* *}) \
\hline & \text { Sig. (two-tailed) } & & 0.005 \
\hline & N & 100 & 100 \
\hline \begin{array}{l}
\text { Adverting } \
\text { expenditure }
\end{array} & \text { Pearson correlation } & 0.753 (^{* *})& 1 \
\hline & \text { Sig. (two-tailed) } & 0.000 & \
\hline & N & 100 & 100 \
\hline
\end{array}$ ** Correlation is significant at the 0.01 level (two-tailed).

Accepted Answer

A)  about 75 per cent of variance in sales can be explained by the variance in advertising expenditure. 
B)  about 57 per cent of the variance in advertising expenditure can be explained by the variance in sales. 
C)  about 57 per cent of the variance in sales can be explained by the variance in advertising expenditure. 
D)  about 75 per cent of the variance in advertising expenditure can be explained by the variance in sales.

Question 13

The Chi-square test is typically used for nominal variables which are dichotomous in nature.

Accepted Answer

A) True 
 B)False

Question 14

The Chi-square test involves comparing ________ frequencies with the ________ frequencies.

Accepted Answer

A)  observed; actual 
B)  expected; predicted 
C)  expected; forecast 
D)  observed; expected

Question 15

The statistical significance of a correlation can be tested using the t-test.

Accepted Answer

A) True 
 B)False

Question 16

In a regression equation, the slope of the line F1F1F1S1F1F1F10 is the change in Y that occurs due to a corresponding change of one unit of X.

Accepted Answer

A) True 
 B)False

Question 17

To calculate the expected frequencies for the cells in a cross tabulation, the actual observed numbers of respondents in each individual cell is required.

Accepted Answer

A) True 
 B)False

Question 18

The appropriate statistical test to use to calculate the association between two nominal variables is:

Accepted Answer

A)  Spearman's rank correlation 
B)  regression analysis. 
C)  Chi-square test. 
D)  correlation analysis.

Question 19

Bivariate linear regression investigates the relationship between a dependent variable and two independent variables.

Accepted Answer

A) True 
 B)False

Question 20

The regression outputs for sales and number of salespeople are shown below. Model summary
$$\begin{array} { | l | l | r | r | r | } 
\hline \text { Model } & \boldsymbol { R } & \boldsymbol { R } \text {-square } & \begin{array} { c } 
\text { Adjusted } \
\boldsymbol { R } \text {-square }
\end{array} & \begin{array} { r } 
\text { Std. error of } \
\text { the estimate }
\end{array} \
\hline 1 & .201 \text { (a) } & .04 & .342 & 56.823 \
\hline
\end{array}$$ a Predictors: (Constant), number of salespeople
ANOVA(b)
$\begin{array}{|l|l|r|r|r|r|r|}
\hline \text { Model } && {\begin{array}{c}
\text { Sum of } \
\text { squares }
\end{array}} & \text { df } & \text { Mean square } &  {F} & {\text { Sig. }} \
\hline 1 & \text { Regression } & 77152.238 & 1 & 77152.238 & 35.117 & .057(\mathrm{a}) \
\hline & \text { Residual } & 61516.962 & 28 & 2197.034 & & \
\hline & \text { Total } & 138669.200 & 29 & & & \
\hline
\end{array}$ a Predictors: (Constant), number of salespeople
B Dependent variable: Sales (A$'000)
Coefficients(a)
$$\begin{array} { | l | l | cr | r | r | r |} 
\hline\text { Model } & &  { \begin{array} { c } 
\text { Unstandardised } \
\text { coefficients }
\end{array} } && \begin{array} { c } 
\text { Standardised } \
\text { coefficients }
\end{array} & { \boldsymbol { t } } & { \text { Sig. } } \
\hline & & \boldsymbol { B } & \text { Std. Error } & \text { Beta } & & \
\hline 1 & \text { (Constant) } & 72.612 & 9.203 & & 2.565 & .013 \
\hline & \text { Number of salespeople } & 35.623 & 3.296 & .201 & 5.926 & .064 \
\hline
\end{array}$$ a Dependent variable: Sales (A$'000)
The above shows that:

Accepted Answer

A)  for every one-unit increase in number of salespeople, average sales will increase by approximately 73 units 
B)  the regression results suggested a good model fit 
C)  the observed results occurred as a result of sampling error 
D)  the regression coefficient is significant

Exam 14: Bivariate Statistical Analysis: Tests of Association

In correlation analysis, the strength of the association between the variables under investigation is determined by:

Which of the following is not true for regression?

When examining regression results, how well the model fits the data is determined by consulting the:

The mathematical symbol Y is commonly used for the independent variable, and X typically denotes the dependent variable.

The coefficient of determination, r², ranges from:

To use the Chi-square test, both variables in a 2 x 2 contingency table must be measured on a ratio or interval scale.

A correlation matrix can quickly give the researcher an overview of the direction, strength and statistical significance of each paired relationship.

To compute the Chi-square value for the contingency table, the researcher must first identify an expected distribution for that table.

In correlation analysis, if associated values of the two variables differ from their means in the same direction, their covariance will be negative.

A Spearman's rank-order correlation coefficient examines the relationship between two ordinal variables.

The Chi-square test is typically used for nominal variables which are dichotomous in nature.

The Chi-square test involves comparing frequencies with the frequencies.

The statistical significance of a correlation can be tested using the t-test.

In a regression equation, the slope of the line  is the change in Y that occurs due to a corresponding change of one unit of X.

To calculate the expected frequencies for the cells in a cross tabulation, the actual observed numbers of respondents in each individual cell is required.

The appropriate statistical test to use to calculate the association between two nominal variables is:

Bivariate linear regression investigates the relationship between a dependent variable and two independent variables.