Q: A researcher finds $$r = 0.624$$ between 'opportunity to learn new things' and 'satisfaction with supervisor.' What percentage of variance in satisfaction is explained by opportunity to learn new things?

$$0.624^2$$ \times 100 = 38.9\%$$

Q: Which hypothesis is tested in a two-tailed test for the significance of a correlation coefficient?

$$H_0$$: \rho = 0$$; H_a$$: \rho \neq 0$$

Question 1

Which of the following best describes the meaning of the correlation coefficient $$r$$?

Accepted Answer

It measures the strength and direction of a linear relationship between two variables.

Question 2

Given the regression equation $$\hat{y} = 68.08 + 6.237x$$, what does the slope $$6.237$$ represent in the context of predicting exam grades from hours studied?

Accepted Answer

For each additional hour studied, the predicted exam grade increases by 6.237 points.

Question 3

If the correlation coefficient $$r = -0.85$$, which scatterplot pattern would you expect to see?

Accepted Answer

A strong negative linear correlation, where as $$x$$ increases, $$y$$ tends to decrease.

Question 4

What is the coefficient of determination ($$R^2) $$and what does it tell us?

Accepted Answer

$$R^2 is $$the proportion of variance in the dependent variable that is explained by the independent variable.

Question 5

In the context of regression, what does the intercept $$a$$ represent in the equation $$\hat{y} = a + bx$$?

Accepted Answer

The predicted value of $$y$$ when $$x = 0.$$

Question 6

Which of the following is NOT an assumption of the Pearson Product-Moment correlation?

Accepted Answer

The relationship between $$x$$ and $$y is $$nonlinear.

Question 7

A researcher finds $$r = 0.624$$ between 'opportunity to learn new things' and 'satisfaction with supervisor.' What percentage of variance in satisfaction is explained by opportunity to learn new things?

Accepted Answer

$$0.624^2$$ 	imes 100 = 38.9\%$$

Question 8

Which hypothesis is tested in a two-tailed test for the significance of a correlation coefficient?

Accepted Answer

$$H_0$$: ho = 0$$; H_a$$: ho 
eq 0$$

Question 9

Which of the following statements about correlation and causation is correct?

Accepted Answer

A significant correlation does not imply causation.

Question 10

Given the following ANOVA table for a regression model:

Regression SS = 1671.410, Residual SS = 2625.556, Total SS = 4296.967

What is the $$R^2$$ value for this model?

Accepted Answer

$$R^2$$ = \frac{1671.410}{4296.967} = 0.389$$

Question 11

Which scenario below is an example of a spurious correlation?

Accepted Answer

Ice cream sales at the beach correlating with the number of shark attacks.

Question 12

If the standardized regression coefficient $$\beta = 0.790$$, what does this mean?

Accepted Answer

A one standard deviation increase in $$x is $$associated with a 0.790 standard deviation increase in $$y.$$

Question 13

Which of the following is the correct formula for the $$t-$$statistic to test the significance of a correlation coefficient $$r$$ with $$n$$ data pairs?

Accepted Answer

$$t = \frac{r \sqrt{n-2}}{\sqrt{1-r^2$}}$$

Question 14

A scatterplot shows points forming a clear upward trend from left to right. Which type of correlation does this indicate?

Accepted Answer

Positive linear correlation

Question 15

Which of the following would be an appropriate use of multiple regression?

Accepted Answer

To determine which of several predictors best explains PTSD among first responders.

Question 16

If $$r = 0$$, what can we conclude about the relationship between $$x$$ and $$y$$?

Accepted Answer

There is no linear relationship between $$x$$ and $$y.$$

Question 17

Which of the following is a correct interpretation of the standard error of the estimate in regression output?

Accepted Answer

It is the typical distance that the observed values fall from the regression line.

Question 18

If the $$p-$$value for the regression slope is less than $$0.05$$, what does this indicate?

Accepted Answer

There is a statistically significant relationship between the predictor and outcome variable.

Question 19

Which of the following would violate the assumptions of simple linear regression?

Accepted Answer

The relationship between $$x$$ and $$y is $$curvilinear.

Question 20

In the regression output, the standardized coefficient (Beta) for 'Opportunity to learn new things' is $$0.624. $$What does this mean?

Accepted Answer

A one standard deviation increase in opportunity to learn new things is associated with a $$0.624$$ standard deviation increase in satisfaction with supervisor.

Chapter 9: Correlation and Regression – Study Notes

스터디 가이드 - 연습 문제

학습 가이드 - 플래시카드