Q: Given the regression equation $$y = 19.41 + 4.29x$$, where $$x is $$age in years and $$y is $$weight in pounds, what is the predicted weight for a child who is 10 years old?

$$y = 19.41 + 4.29 \times 10 = 62.31$$ pounds

Q: Given the regression equation $$y = 19.41 + 4.29x$$, what is the residual for a child who is 9 years old and weighs 50 pounds?

Residual $$= 50 - (19.41 + 4.29 \times 9) = 50 - 58.02 = -8.02$$

Question 1

Which of the following best describes the correlation coefficient $$r$$ for a scatterplot that shows a strong, positive, linear relationship between two variables?

Accepted Answer

$$r = 0.92$$

Question 2

Given the regression equation $$y = 19.41 + 4.29x$$, where $$x is $$age in years and $$y is $$weight in pounds, what is the predicted weight for a child who is 10 years old?

Accepted Answer

$$y = 19.41 + 4.29 	imes 10 = 62.31$$ pounds

Question 3

If the correlation coefficient $$r is $$negative, what can you say about the slope of the least-squares regression line?

Accepted Answer

The slope will be negative.

Question 4

Which of the following statements about extrapolation is correct?

Accepted Answer

Extrapolation is predicting $$y$$ values for $$x$$ values outside the range of the data.

Question 5

A residual plot shows a clear curved pattern. What does this indicate about the appropriateness of a linear model?

Accepted Answer

A linear model is not appropriate.

Question 6

If the coefficient of determination $$r^2 is$$ $$0.853$$, what does this mean in the context of a regression analysis?

Accepted Answer

About $$85.3\% of $$the variation in $$y is $$explained by the variation in $$x.$$

Question 7

Which of the following is a correct interpretation of a positive correlation between two variables?

Accepted Answer

As one variable increases, the other variable tends to increase.

Question 8

Given the regression equation $$y = 19.41 + 4.29x$$, what is the residual for a child who is 9 years old and weighs 50 pounds?

Accepted Answer

Residual $$= 50 - (19.41 + 4.29 	imes 9) = 50 - 58.02 = -8.02$$

Question 9

Which variable is typically considered the explanatory variable in a study of age and weight?

Accepted Answer

Age

Question 10

A correlation coefficient $$r = 0$$ indicates which of the following?

Accepted Answer

There is no linear relationship between the variables.

Question 11

If a regression line is used to predict the weight of a 20-year-old, but the data only includes ages up to 15, what is this an example of?

Accepted Answer

Extrapolation

Question 12

Which of the following best describes the relationship between $$r$$ and $$r^2$$?

Accepted Answer

$$r^2 is $$the square of the correlation coefficient $$r.$$

Question 13

A study finds $$r = -0.926$$ between hours spent watching TV and exam scores. What does this indicate?

Accepted Answer

There is a strong negative linear relationship.

Question 14

Which of the following is NOT a property of the correlation coefficient $$r$$?

Accepted Answer

$$r$$ measures the strength of any relationship, linear or not.

Question 15

If the regression equation is $$y = 19.41 + 4.29x$$, what does the value $$4.29$$ represent?

Accepted Answer

The average increase in $$y$$ for each additional unit of $$x.$$

Introductory Statistics Study Guide: Correlation, Regression, and Data Analysis

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