Question

Question 2

Pearson's correlation coefficient open parentheses r close parentheses is considered a symmetric measure because:


Question options:

its values range from 0 to 1.

it indicates the causal relationship between two variables.

the sign of r is the same as the sign of the regression coefficient.

it will be the same regardless of which variable is the x and which is the y.


Question 3

A proper interpretation for r squared equals r^2 = 0. 754 is:


Question options:

75. 4% of the variation in the response variable can be explained by our knowledge of the explanatory variable.

the amount of variation in the response variable is reduced by 24. 6%.

for each unit increase in the explanatory variable, the response variable increases by 75. 4%.

None of the above.


Question 7

Suppose that you have a bivariate data set and the correlation coefficient for the relationship between x and y is strong. Suppose also that you compute a least-squares regression line that seems to fit the linear pattern in this bivariate data. You decide to plot the observed x-values (along the x-axis) against the residuals (along the y-axis). If the pattern in the data is truly linear, you should find that the residuals:


Question options:

follow a u-shaped pattern.

are randomly distributed around the line y minus y with hat on top equals 0.

are clumped at values above the line y minus y with hat on top equals 0.

Do all of the above.


Question 9

An outlier point is added to a set of bivariate data. In what way must your analysis change with the addition of the outlier?


Question options:

The sign of the regression coefficient will change from positive to negative, or vice versa.

The value of the correlation coefficient will move closer to 0.

The regression constant will change dramatically.

All of the above.


Question 15

The correlation between variables x and y is 0. 50. You compute a least-squares regression line with this bivariate data. Which of the following must be true?


Question options:

The r squared is greater than 0. 50.

The regression constant (or y-intercept) is positive.

The regression coefficient is positive.

The slope of the regression line is negative

Answer 1

Based on my expertise in statistics, here are the answers to the multiple choice questions:

Question 2:

The correct answer is: it will be the same regardless of which variable is the x and which is the y.

Pearson's correlation coefficient r is a symmetric measure, meaning it does not depend on which variable is considered x and which is y. The value of r remains unchanged if you swap the variables.

Question 3:

The correct answer is: 75.4% of the variation in the response variable can be explained by our knowledge of the explanatory variable.

An R-squared of 0.754 means 75.4% of the variation in the response variable is accounted for by the explanatory variable through the linear regression model.

Question 7:

The correct answer is: are randomly distributed around the line y - ŷ = 0

If the residuals plotted against the x-values show a random scatter around the zero line, it indicates the data fit the linear pattern well.

Question 9:

The correct answer is: The value of the correlation coefficient will move closer to 0.

Adding an outlier will reduce the strength of the correlation between the two variables.

Question 15:

The correct answer is: The r squared is greater than 0.50

If correlation r is 0.50, the R-squared must be greater than 0.50 since R-squared is the square of the correlation r.