Question 1

The coefficient of determination may range in values between negative one and positive one.

Accepted Answer

The coefficient of determination (R-squared) ranges in values between zero and one. It cannot be negative.

Question 2

The coefficient of correlation indicates the direction and the strength of the linear relationship between two variables.

Accepted Answer

The coefficient of correlation measures the degree to which two variables are linearly related and indicates the direction and strength of their relationship.

Question 3

The coefficient of determination measures the percentage of variation in the independent variable explained by the dependent variable.

Accepted Answer

The coefficient of determination measures the percentage of variation in the dependent variable explained by the independent variable.

Question 4

A basketball player has the following points for seven games: 20, 25, 32, 18, 19, 22, 30. Compute the following measures of central location and variability:
a. mean.
b. median.
c. standard deviation.
d. coefficient of variation.

Accepted Answer

The answer of A basketball player has the following points...

Question 5

Monthly rent data in dollars for a sample of 10 one-bedroom apartments in Perth are given below: $$\begin{array} { | l | l | l | l | l | l | l | l | l | l | } 
\hline 220 & 200 & 230 & 215 & 235 & 250 & 260 & 210 & 265 & 250 \
\hline
\end{array}$$ a. Compute the sample monthly average rent.
b. Compute the sample median.
c. What is the mode?

Accepted Answer

The answer of Monthly rent data in dollars for a...

Question 6

The coefficient of correlation is the covariance between the two variables divided by the standard deviations of the two variables.

Accepted Answer

This is the formula for calculating the coefficient of correlation (also known as Pearson's correlation coefficient).

Question 7

The following data represent the numbers of bedrooms in a sample of 10 suburban houses in Mel-bourne:
$$\begin{array} { | r | r | r | r | r | r | r | r | r | r | } 
\hline 3 & 3 & 2 & 2 & 4 & 5 & 2 & 5 & 4 & 2 \
\hline
\end{array}$$
Use these data to answer the following question/s.

-a. Compute the mean.
b. Compute the median.

Accepted Answer

The answer of The following data represent the numbers of...

Question 8

If the coefficient of correlation r = 0, then there is no linear relationship between the dependent variable y and the independent variable x.

Accepted Answer

A correlation coefficient of 0 indicates no linear relationship between the variables.

Question 9

Generally speaking, if two variables have a strong positive linear relationship, the covariance between them is equal to one.

Accepted Answer

The covariance between two variables with a strong positive linear relationship may be positive, but it is not necessarily equal to one. The value of covariance depends on the magnitude and variability of the variables being measured.

Question 10

When approximating descriptive measures for grouped data, the sample mean can be obtained by making the assumption that the midpoint of each class closely approximates the mean of each class.

Accepted Answer

This is true since the sample mean is calculated by summing up the product of the midpoint of each class and its frequency, and dividing it by the total frequency of all classes. This assumes that the midpoint is a good approximation for the mean of each class.

Question 11

The following data represent the numbers of bedrooms in a sample of 10 suburban houses in Mel-bourne:
$$\begin{array} { | r | r | r | r | r | r | r | r | r | r | } 
\hline 3 & 3 & 2 & 2 & 4 & 5 & 2 & 5 & 4 & 2 \
\hline
\end{array}$$
Use these data to answer the following question/s.

-Compute the coefficient of variation.

Accepted Answer

The answer of The following data represent the numbers of...

Question 12

If the coefficient of correlation r = +1, then the best-fit linear equation will actually be satisfied by all of the data points.

Accepted Answer

A correlation coefficient of +1 represents a perfect positive linear relationship between two variables. This means that all data points would fall exactly on a straight line, and the best-fit linear equation would pass through every single point. Therefore, the statement is true.

Question 13

The coefficient of determination lies between 0 and 1 (both inclusive).

Accepted Answer

The coefficient of determination, also known as R-squared, is a measure of how well the regression line fits the data. It is always between 0 and 1, inclusive. A value of 0 indicates that the regression line does not fit the data at all, while a value of 1 indicates a perfect fit.

Question 14

A sample of 25 families was asked how many pets they owned. Their responses are summarized in the following table. $$\begin{array} { | l | r | r | r | r | r | r | } 
\text { Number of pets } & 0 & 1 & 2 & 3 & 4 & 5 \
\hline \text { Number of families } & 3 & 10 & 5 & 4 & 2 & 1 \
\hline
\end{array}$$ a. Determine the mean, the median and the mode of the number of pets owned per family.
b. Describe briefly what each statistic in part (a) tells you about the data.

Accepted Answer

The answer of A sample of 25 families was asked...

Question 15

The following data represent the numbers of bedrooms in a sample of 10 suburban houses in Mel-bourne:
$$\begin{array} { | r | r | r | r | r | r | r | r | r | r | } 
\hline 3 & 3 & 2 & 2 & 4 & 5 & 2 & 5 & 4 & 2 \
\hline
\end{array}$$
Use these data to answer the following question/s.

-a. Compute the range.
b. Compute the variance.
c. Compute the standard deviation.

Accepted Answer

The answer of The following data represent the numbers of...

Question 16

The shape of the distribution helps to determine the best measure of central location and variability in a data set.

Accepted Answer

The shape of the distribution (such as being symmetric or skewed) can affect the accuracy and usefulness of certain measures of central location (such as mean versus median) and variability (such as standard deviation versus interquartile range). Therefore, it is important to consider the shape of the distribution when choosing the appropriate measures for analyzing the data.

Question 17

The coefficient of correlation is always the same value as the coefficient of determination.

Accepted Answer

The coefficient of determination is the square of the coefficient of correlation. Therefore, they cannot be the same value.

Question 18

When approximating descriptive measures for grouped data, the shape of the distribution within each class is ignored.

Accepted Answer

The answer of When approximating descriptive measures for grouped data,...

Question 19

What are the relative magnitudes of the mean, median and mode for a unimodal distribution that is:
a. symmetrical?
b. skewed to the left?
c. skewed to the right?

Accepted Answer

The answer of What are the relative magnitudes of the...

Question 20

The least squares method is the method of deriving a linear equation between two numerical variables.

Accepted Answer

The least squares method is a statistical technique used to find the line of best fit for a set of data points. This line can be used to make predictions and analyze the relationship between two variables. It is commonly used in finance, economics, and engineering.

Quiz 5: Numerical Descriptive Measures

The coefficient of determination may range in values between negative one and positive one.

The coefficient of correlation indicates the direction and the strength of the linear relationship between two variables.

The coefficient of determination measures the percentage of variation in the independent variable explained by the dependent variable.

A basketball player has the following points for seven games: 20, 25, 32, 18, 19, 22, 30. Compute the following measures of central location and variability: a. mean. b. median. c. standard deviation. d. coefficient of variation.

The coefficient of correlation is the covariance between the two variables divided by the standard deviations of the two variables.

If the coefficient of correlation r = 0, then there is no linear relationship between the dependent variable y and the independent variable x.

Generally speaking, if two variables have a strong positive linear relationship, the covariance between them is equal to one.

When approximating descriptive measures for grouped data, the sample mean can be obtained by making the assumption that the midpoint of each class closely approximates the mean of each class.

If the coefficient of correlation r = +1, then the best-fit linear equation will actually be satisfied by all of the data points.

The coefficient of determination lies between 0 and 1 (both inclusive).

The shape of the distribution helps to determine the best measure of central location and variability in a data set.

The coefficient of correlation is always the same value as the coefficient of determination.

When approximating descriptive measures for grouped data, the shape of the distribution within each class is ignored.

What are the relative magnitudes of the mean, median and mode for a unimodal distribution that is: a. symmetrical? b. skewed to the left? c. skewed to the right?

The least squares method is the method of deriving a linear equation between two numerical variables.