Question 1

The Pearson's correlation coefficient is actually a standardised measure of __________.

Accepted Answer

The answer of The Pearson's correlation coefficient is actually a...

Question 2

The square of the correlation coefficient is called the ___________ of _____________.

Accepted Answer

The answer of The square of the correlation coefficient is...

Question 3

Two groups of students - those looking to study science degrees and those looking to study business degrees - are asked to rank, in order of preference, the universities they are applying for. The researcher then wants to determine the correlation between the two groups. Which statistical test is most appropriate?
A) Pearson's correlation coefficient
B) Chi-square test
C) Spearman's rank-order correlation coefficient
D) Independent samples t-test

Accepted Answer

Since the data is ranked in order of preference, it is not interval data and therefore Pearson's correlation coefficient and independent samples t-test are not appropriate. Chi-square test is used for nominal data, which does not apply here. Therefore, the most appropriate test for this scenario is Spearman's rank-order correlation coefficient.

Question 4

In a regression equation, if the average value of Y is 15.6, the average value of X is 5.3, and the y-intercept is 8.5, then the slope is approximately:
A) 1.13.
B) 1.21.
C) 4.55.
D) 1.34.

Accepted Answer

Using the equation of a straight line, y = mx + b, we know that b (the y-intercept) is 8.5.

We also know that the average value of Y is 15.6 and the average value of X is 5.3.

Thus, we can set up the equation:

15.6 = m(5.3) + 8.5

Solving for m:

15.6 - 8.5 = 5.3m

7.1 = 5.3m

m ≈ 1.34

Therefore, the slope is approximately 1.34.

Question 5

If the correlation between two variables is -0.64, then the coefficient of determination is approximately ____.

Accepted Answer

The answer of If the correlation between two variables is...

Question 6

If sales of baby strollers are associated with the number of babies born during the few months prior to the sales period, then the sales volume of baby strollers is the _________ variable and the number of babies born is the ___________ variable.

Accepted Answer

The answer of If sales of baby strollers are associated...

Question 7

When examining the correlation matrix, the p-value indicates the ___________ ____________ of the association.

Accepted Answer

The answer of When examining the correlation matrix, the p-value...

Question 8

The Chi-square test involves comparing ________ frequencies with the ________ frequencies.
A) observed; actual
B) expected; predicted
C) expected; forecast
D) observed; expected

Accepted Answer

The Chi-square test involves comparing observed frequencies with expected frequencies.

Question 9

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)
$$\begin{array} { | l | l | c | r | r | r | r | } 
\hline \text { Model } & & \begin{array} { c } 
\text { Sum of } \
\text { squares }
\end{array} &\text{ df} & \text { Mean square } & \boldsymbol { F } & { \text { Sig. } } \
\hline 1 & \text { Regression } & 77152.238 & 1 & 77152.238 & 35.117 & .057 ( \mathrm { a } ) \
\hline & \text { Residual } & 61516.962 & 28 & 2197.034 & & \
\hline & \text { Total } & 138669.200 & 29 & & & \
\hline
\end{array}$$ a Predictors: (Constant), number of salespeople
B Dependent variable: Sales (A$'000)
Coefficients(a)
$$\begin{array} { | l | l | c | r | r | r | r| } 
\hline \text { Model } & &{ \begin{array} { c } 
\text { Unstandardised } \
\text { coefficients }
\end{array} } & \begin{array} { c } 
\text { Standardised } \
\text { coefficients }
\end{array} & { \boldsymbol { t } } &  { \text { Sig. } } \
\hline & & \boldsymbol { B } & \text { Std. Error } & \text { Beta } & & \
\hline 1 & \text { (Constant) } & 72.612 & 9.203 & & 2.565 & .013 \
\hline & \text { Number of salespeople } & 35.623 & 3.296 & .201 & 5.926 & .064 \
\hline
\end{array}$$ a Dependent variable: Sales (A$'000)
The above shows that:
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

Accepted Answer

The p-value for the regression coefficient of the number of salespeople is 0.064, which is greater than the common significance level of 0.05, indicating that the coefficient is not statistically significant. The observed results may be due to sampling error.

Question 10

A __________ test is typically used to test for association between two nominal variables.

Accepted Answer

The answer of A __________ test is typically used to...

Question 11

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)
$$\begin{array} { | l | l | r | r | r | r | r | } 
\hline \text { Model } & & \begin{array} { c } 
\text { Sum of } \
\text { Squares }
\end{array} & { \boldsymbol { df } } & \text { Mean square } & \boldsymbol { F } & { \text { Sig. } } \
\hline 1 & \text { Regression } & 77152.238 & 1 & 77152.238 & 35.117 & .000 ( \mathrm { a } ) \
\hline & \text { Residual } & 61516.962 & 28 & 2197.034 & & \
\hline & \text { Total } & 138669.200 & 29 & & & \
\hline
\end{array}$$ a Predictors: (Constant), number of salespeople
B Dependent Variable: Sales (A$'000)
Coefficients(a)
$$\begin{array} { | l | l | c | r | r | r | r| } 
\hline \text { Model } & &{ \begin{array} { c } 
\text { Unstandardised } \
\text { coefficients }
\end{array} } & \begin{array} { c } 
\text { Standardised } \
\text { coefficients }
\end{array} & { \boldsymbol { t } } &  { \text { Sig. } } \
\hline & & \boldsymbol { B } & \text { Std. Error } & \text { Beta } & & \
\hline 1 & \text { (Constant) } & 72.612 & 9.203 & & 2.565 & .013 \
\hline & \text { Number of salespeople } & 35.623 & 3.296 & .746 & 5.926 & .000\
\hline
\end{array}$$ 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:
A) 36 units.
B) 73 units.
C) 75 units.
D) 108 units.

Accepted Answer

For every one-unit increase in number of salespeople, average sales will increase by approximately 36 units.

Question 12

A __________ ____ correlation coefficient is typically used to test for association between two ordinal variables.

Accepted Answer

The answer of A __________ ____ correlation coefficient is typically...

Question 13

The ___________ coefficient, r, ranges from +1 to -1.

Accepted Answer

The answer of The ___________ coefficient, r, ranges from +1...

Question 14

It is a requirement in correlation analysis that both variables to be tested are ________ or _____ in nature.

Accepted Answer

The answer of It is a requirement in correlation analysis...

Question 15

A research hypothesis states that male university students are more likely to study STEM courses than female university students. Thus, the researcher would like test to see if an association exists between gender and area of study. Which statistical test is most appropriate?
A) Pearson's correlation coefficient
B) Chi-square test
C) Spearman's rank-order correlation coefficient
D) Independent samples t-test

Accepted Answer

The most appropriate statistical test for testing the association between gender and area of study is the chi-square test. This test is used to determine if there is a significant difference between the expected frequencies and the observed frequencies. In this scenario, the researcher wants to determine if there is a significant difference in the number of male and female university students studying STEM courses. The chi-square test is suitable for testing the relationship between categorical variables, making it the best choice for this research hypothesis.

Question 16

'Tests of ___________' is a general term which refers to a number of bivariate statistical techniques used to test the nature of the relationship between the variables.

Accepted Answer

The answer of 'Tests of ___________' is a general term...

Question 17

A Spearman's rank-order correlation coefficient is a technique used when determining the correlation between two _______ scaled variables.
A) nominal
B) interval
C) ordinal
D) ratio

Accepted Answer

Spearman's rank-order correlation coefficient is used when the variables being correlated are measured on an ordinal scale, where the values can be ranked but not necessarily compared in terms of magnitude. It is not appropriate for nominal variables (where the values are just labels), interval variables (where the values have a specific numerical meaning but lack a true zero point), or ratio variables (where the values have a true zero point and can be meaningfully compared in terms of magnitude).

Question 18

If the relationship between two variables is such that both variables are caused by a third variable, then the original relationship between the first two variables is said to be __________ _______.

Accepted Answer

The answer of If the relationship between two variables is...

Question 19

A correlation coefficient indicates both the _________ of the relationship between two variables and the _________ of this relationship.

Accepted Answer

The answer of A correlation coefficient indicates both the _________...

Question 20

The regression output for sales and advertising spend is shown below. Model summary
$$\begin{array} { | l | l | r | r | r | } 
\hline \text { Model } & \boldsymbol { R } & \boldsymbol { R } \text {-square } & \begin{array} { c } 
\text { Adjusted } \
\boldsymbol { R } \text {-square }
\end{array} & \begin{array} { r } 
\text { Std. error of } \
\text { the estimate }
\end{array} \
\hline 1 & .445 \text { (a) } & .198 & .169 & 1229.780 \
\hline
\end{array}$$ a Predictors: (Constant), advertising spend
ANOVA(b)
$$\begin{array} { | l | l | r | r | r | r | c | } 
\hline \text { Model } & & \begin{array} { c } 
\text { Sum of } \
\text { squares }
\end{array} & \text { df } & \text { Mean square } & { \boldsymbol { F } } & \text { Sig. } \
\hline 1 & \text { Regression } & 10448599.647 & 1 & 10448599.647 & 6.909 & .014 ( \mathrm { a } ) \
\hline & \text { Residual } & 42346067.019 & 28 & 1512359.536 & & \
\hline & \text { Total } & 52794666.667 & 29 & & & \
\hline
\end{array}$$ a Predictors: (Constant), advertising spend
B Dependent variable: Sales (A$'000)
Coefficients(a)
$$\begin{array} { | l | l | c | r | r | r | r| } 
\hline \text { Model } & &{ \begin{array} { c } 
\text { Unstandardised } \
\text { coefficients }
\end{array} } & \begin{array} { c } 
\text { Standardised } \
\text { coefficients }
\end{array} & { \boldsymbol { t } } &  { \text { Sig. } } \
\hline & & \boldsymbol { B } & \text { Std. Error } & \text { Beta } & & \
\hline 1 & \text { (Constant) } & 2993.298&706.247&&4.238&.000 \
\hline & \text { Number of salespeople } & 42.928&16.332&.445&2.628&.014\
\hline
\end{array}$$ a Dependent variable: Sales (A$'000)
The above shows that:
A) approximately 45 per cent of the variance in sales can be explained by advertising spend.
B) approximately 43 per cent of the variance in Sales can be explained by advertising spend.
C) approximately 14 per cent of the variance in sales can be explained by advertising spend.
D) approximately 20 per cent of the variance in sales can be explained by advertising spend.

Accepted Answer

The R-square value is 0.198, which indicates that approximately 19.8% (or 20% when rounded) of the variance in sales can be explained by advertising spend.

Quiz 14: Bivariate Statistical Analysis: Tests of Association

The Pearson's correlation coefficient is actually a standardised measure of __________.

The square of the correlation coefficient is called the _ of ___.

In a regression equation, if the average value of Y is 15.6, the average value of X is 5.3, and the y-intercept is 8.5, then the slope is approximately:

If the correlation between two variables is -0.64, then the coefficient of determination is approximately ____.

If sales of baby strollers are associated with the number of babies born during the few months prior to the sales period, then the sales volume of baby strollers is the _ variable and the number of babies born is the ___ variable.

When examining the correlation matrix, the p-value indicates the _ __ of the association.

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

A __________ test is typically used to test for association between two nominal variables.

A ______ correlation coefficient is typically used to test for association between two ordinal variables.

The ___________ coefficient, r, ranges from +1 to -1.

It is a requirement in correlation analysis that both variables to be tested are ____ or _ in nature.

A research hypothesis states that male university students are more likely to study STEM courses than female university students. Thus, the researcher would like test to see if an association exists between gender and area of study. Which statistical test is most appropriate?

'Tests of ___________' is a general term which refers to a number of bivariate statistical techniques used to test the nature of the relationship between the variables.

A Spearman's rank-order correlation coefficient is a technique used when determining the correlation between two _______ scaled variables.

If the relationship between two variables is such that both variables are caused by a third variable, then the original relationship between the first two variables is said to be ____ _.

A correlation coefficient indicates both the _ of the relationship between two variables and the _ of this relationship.