Q: Given the regression output for Satisfaction with Supervisor (fifth image), what is the predicted satisfaction score for an employee with an opportunity to learn new things score of 5?

$$\hat{y} = 25.174 + 0.607 \times 5 = 28.209$$

Question 1

Which of the following best describes the relationship shown in the top right scatterplot of the first image?

Accepted Answer

Positive linear correlation

Question 2

Given the regression output for predicting Exam Grade from Hours Studied (second image), what is the value of the coefficient of determination, and what does it represent?

Accepted Answer

$$R^2 = 0.625$, which means 62.5\% of the variance in exam grades is explained by hours studied.

Question 3

In the ANOVA table for the regression of Exam Grade on Hours Studied (third image), what does the significance value (Sig.) indicate?

Accepted Answer

There is a statistically significant relationship between hours studied and exam grade.

Question 4

Based on the coefficients table for predicting Exam Grade from Hours Studied (fourth image), what is the regression equation?

Accepted Answer

$$\hat{y} = 68.080 + 6.237x$$

Question 5

What does the standardized coefficient (Beta) represent in the regression output?

Accepted Answer

The expected change in y for a one standard deviation change in x.

Question 6

If the correlation coefficient $$r$$ between two variables is $$-0.85$$, what can you conclude?

Accepted Answer

There is a strong negative linear relationship.

Question 7

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

Accepted Answer

Variables must be categorical.

Question 8

What is the null hypothesis when testing the significance of a correlation coefficient?

Accepted Answer

$$H_0$$: \rho = 0$$

Question 9

If $$r^2 = 0.389$ in a regression analysis (see fifth image), what does this mean?

Accepted Answer

38.9\% of the variance in the dependent variable is explained by the predictor.

Question 10

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

Accepted Answer

Correlation does not imply causation.

Question 11

Given the regression output for Satisfaction with Supervisor (fifth image), what is the predicted satisfaction score for an employee with an opportunity to learn new things score of 5?

Accepted Answer

$$\hat{y} = 25.174 + 0.607 	imes 5 = 28.209$$

Question 12

Which test statistic is used to test the significance of a correlation coefficient?

Accepted Answer

t-test

Question 13

What is a spurious correlation?

Accepted Answer

A correlation that occurs by chance or due to a common cause, not a direct relationship.

Question 14

If the regression coefficient $$b$$ for a predictor is not significantly different from zero, what does this imply?

Accepted Answer

The predictor variable does not significantly contribute to predicting the outcome.

Question 15

Which scenario best illustrates a violation of the linearity assumption in correlation analysis?

Accepted Answer

A scatterplot where points form a U-shaped pattern.

Question 16

What is the formula for the t-statistic used 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 17

Which of the following is true about the coefficient of determination ($$r^2$$)?

Accepted Answer

It represents the proportion of variance in y explained by x.

Question 18

In a regression analysis, what does the intercept (constant) represent?

Accepted Answer

The expected value of y when x is zero.

Question 19

If you have ordinal data and want to measure correlation, which statistic should you use?

Accepted Answer

Spearman's $$\rho$$

Question 20

Which of the following best describes the meaning of a positive regression coefficient?

Accepted Answer

As the predictor variable increases, the outcome variable tends to increase.

Chapter 9- Correlation and Regression: Concepts, Calculations, and Applications

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