Question 1

Correlation and regression are related statistical functions. Which option best describes this relationship?&#10;A) Regression is a measure of how well correlation explains the relationship between two variables&#10;B) The correlation coefficient always lies on the regression line&#10;C) Correlation can indicate how well the regression line 'fits' the data&#10;D) The regression line can be calculated using values for the mean and the correlation coefficient

Accepted Answer

Correlation indicates the strength and direction of a linear relationship between two variables, while regression involves predicting the value of one variable based on the value of another. The correlation coefficient (r) can indeed indicate how well the regression line fits the data, with values closer to -1 or 1 indicating a stronger fit.

Question 2

Data from established manufacturing companies in Morocco shows that the number of years' experience a sales person has is correlated with their average yearly sales. The correlation coefficient ( r) is 0.62. Calculate, to 1 decimal place, the percentage of variation in sales that is accounted for by experience.

A) 62.0%
B) 61.6%
C) 45.3%
D) 38.4%

38.4%

Accepted Answer

38.4%

Question 3

Which of the following relationships would you expect to be negatively correlated?&#10;A) Marketing budget and Sales revenue&#10;B) Years of experience and Salary&#10;C) Volume of raw materials purchased and Unit cost&#10;D) Car speed and Stopping distance

Accepted Answer

As the volume of raw materials purchased increases, the unit cost typically decreases due to economies of scale, leading to a negative correlation.

Question 4

Which of the following options is not a valid value for the correlation coefficient?&#10;A) -0.94&#10;B) 0&#10;C) 0.36&#10;D) 1.2

Accepted Answer

The correlation coefficient measures the strength and direction of a linear relationship between two variables. Its value ranges from -1 to 1, where -1 indicates a perfect negative linear correlation, 0 indicates no linear correlation, and 1 indicates a perfect positive linear correlation. Therefore, a value of 1.2 is not valid as it falls outside this range.

Question 5

There is a positive correlation between two variables x and y. Which of the following statements is true?&#10;A) As x increases, y will increase&#10;B) As x increases, y will decrease&#10;C) As x increases, y will remain unchanged&#10;D) We cannot say what happens as x increases

Accepted Answer

A positive correlation between two variables x and y means that as one variable increases, the other variable also increases. Therefore, if x increases, y will also increase.

Question 6

What term is used to describe differences in the value of an independent variable which are accounted for by the y on x regression line?&#10;A) Correlated differences&#10;B) Explained differences&#10;C) Unexplained differences&#10;D) Regression differences

Accepted Answer

Explained differences refer to the portion of variability in the dependent variable that can be accounted for by the independent variable(s) in a regression model. This is contrasted with unexplained differences, which represent the variability not accounted for by the model.

Question 7

Which of the following statements is TRUE?&#10;A) Causality normally implies correlation&#10;B) Correlation normally implies causality&#10;C) There is never a relationship between causality and correlation&#10;D) Correlation only occurs when there is causality

Accepted Answer

Causality often leads to correlation because when one variable causes a change in another, this relationship can manifest as a statistical correlation. However, correlation does not necessarily imply causality, as two variables can be correlated due to coincidence, third factors, or other reasons not involving a direct causal relationship.

Question 8

Which of the following options gives the best definition of correlation?&#10;A) An estimate of strength of a relationship between two variables&#10;B) An estimate of the spread of values in a set of data&#10;C) An estimate of skewness in a set of data&#10;D) An estimate of causality between two variables

Accepted Answer

Correlation refers to a statistical measure that expresses the extent to which two variables change together. It provides an estimate of the strength and direction of a relationship between two variables, but it does not imply causation.

Question 9

Which of the following statements about rank correlation is NOT true?&#10;A) Rank correlation is sometimes used to approximate product moment correlation&#10;B) If one variable is non-numeric the rank correlation is most appropriate&#10;C) Rank correlation can be used if variables can be placed in order (e.g. of size)&#10;D) Rank correlation is usually considered to be more accurate than product moment correlation

Accepted Answer

Rank correlation is not usually considered to be more accurate than product moment correlation; it is used in situations where the assumptions for product moment correlation are not met, such as with ordinal data or non-linear relationships.

Question 10

The analysis of two variables indicates a correlation with r = -0.85. Calculate, to 1 decimal place, the percentage of variation in the independent variable that is not accounted for by the dependent variable.

A) 85.0%
B) 72.3%
C) 56.3%
D) 27.8%

Accepted Answer

The percentage of variation not accounted for by the dependent variable is found by subtracting the coefficient of determination (r^2) from 1. Here, r^2 = (-0.85)^2 = 0.7225. Thus, 1 - 0.7225 = 0.2775, or 27.75%, which rounds to 27.8%. However, the correct interpretation is that 72.25% of the variation in the dependent variable is accounted for by the independent variable, meaning 27.75% is not accounted for, which is closest to option D, indicating a mistake in the initial selection and explanation. The correct answer should reflect the unaccounted variation directly related to the question's phrasing, which was misinterpreted in the initial response.

Deck 14: Correlation Techniques