Question 1

Which of the following best describes the difference between correlation and regression?

Accepted Answer

Correlation measures the strength and direction of a linear relationship between two variables, while regression predicts the value of a dependent variable based on an independent variable.

Question 2

Given the regression equation $$	ext{age} = 0.88 + 10.65 	imes 	ext{proportion.black} + 	ext{error}$$, what is the predicted age of a male lion with 60% black nose pigmentation?

Accepted Answer

6.0 years

Question 3

Which of the following is the correct interpretation of a Pearson correlation coefficient $$r = 0.79$$ with a p-value $$\u003c 0.001$$?

Accepted Answer

There is an important, statistically significant linear correlation.

Question 4

In regression analysis, what does the coefficient of determination $$R^2$$ represent?

Accepted Answer

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

Question 5

Which of the following residual plots would indicate a violation of the assumption of constant variance (homoscedasticity)?

Accepted Answer

A plot where the spread of residuals increases as fitted values increase.

Question 6

Which statement is correct regarding the regression output: Multiple $$R^2 = 0.62$?

Accepted Answer

The regression model explained 62% of the variation in age.

Question 7

Which coefficients are significantly different from zero in the regression output below?

Estimate Std. Error t value Pr(\u003e|t|)
(intercept) 0.8790 0.5688 1.545 0.133
proportion.black 10.6471 1.5095 7.053 7.16e-08

Accepted Answer

Only the slope $$b_1$$

Question 8

Which of the following is NOT an assumption of linear regression?

Accepted Answer

The predictor variable must be categorical.

Question 9

A researcher finds a Pearson correlation coefficient $$r = -0.95$$ between two variables. What does this indicate?

Accepted Answer

There is a strong negative linear relationship between the variables.

Question 10

Which test is used to determine if the slope coefficient in a regression model is significantly different from zero?

Accepted Answer

t-test

Question 11

In the context of regression, what does a residual represent?

Accepted Answer

The difference between the observed value and the predicted value for each data point.

Question 12

Which of the following is a reason to check for influential points in regression analysis?

Accepted Answer

Influential points can have a large effect on regression coefficients and model fit.

Question 13

Which of the following is true about the Spearman rank correlation coefficient $$\rho$$?

Accepted Answer

It measures the strength and direction of a monotonic relationship using ranks.

Question 14

Which of the following forms of association is best modeled by simple linear regression?

Accepted Answer

Linear, positive

Question 15

If the residuals from a regression model are not normally distributed, which of the following is a recommended action?

Accepted Answer

Try a transformation of the response variable.

Question 16

Which of the following best describes the goal of estimation in regression analysis?

Accepted Answer

To predict the mean response $$y$$ given a value of $$x$$ using the regression equation.

Question 17

Which of the following is a rule of thumb for a large effect size for correlation according to Cohen (1988)?

Accepted Answer

$$r \u003e 0.5$$

Question 18

A residual plot shows a funnel shape, with residuals spreading out as fitted values increase. What does this indicate?

Accepted Answer

The variance of residuals is not constant (heteroscedasticity).

Question 19

Which of the following is the correct formula for the line of best fit in simple linear regression?

Accepted Answer

$$y = b_0$ + b_1$ x + e$$

Question 20

In the context of regression analysis, what does Cook's distance $$D$$ measure?

Accepted Answer

The influence of a data point on the regression coefficients and fitted values.

Correlation and Regression: Building Statistical Models

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