Question 1

The most common form of simple regression uses:

Accepted Answer

The most common form of simple regression, specifically linear regression, involves two ratio-level variables: one independent variable and one dependent variable. This allows for the calculation of a linear relationship where both variables are measured on a continuous scale.

Question 2

If b=3, the mean of X is 5, and the mean of Y is 10, what is the value of the constant?

Accepted Answer

10 = a + 3(5). Solving for a, we get -5

Question 3

If the slope is 4, the mean of X is 7, and the constant is 3, what is the mean of Y?

Accepted Answer

mean of Y = 3 + 4(7) = 31.

Question 4

When we want to visually examine the relationship between two ratio-level variables, the most common type of graph to use is:

Accepted Answer

When examining the relationship between two ratio-level variables, the most appropriate type of graph would be a scatterplot, which displays individual data points as dots on the graph, allowing for the identification of patterns and trends in the data. Pie and bar graphs are used to display categorical data, while line graphs are typically used to display changes in a single variable over time.

Question 5

If the value of the covariance is negative, which of the following cannot be true?

Accepted Answer

If the covariance is negative, it means that there is an inverse relationship between the two variables. This means that if one variable increases, the other variable decreases. Therefore, the slope cannot be exactly zero as this implies that there is no relationship between the variables. Choices A and B are possible as the slope and correlation coefficient can both be negative in an inverse relationship. Choice D is also possible as a negative covariance does not imply anything about the value of the constant.

Question 6

With simple regression, if we want to know the size of the effect, the best statistic to look at is:

Accepted Answer

The slope in a simple linear regression shows the change in the dependent variable for every one unit change in the independent variable, making it the best statistic to look at for determining the size of the effect. The correlation coefficient (B) shows the strength of the relationship between the variables, but does not indicate the size of the effect. R-squared (C) shows the proportion of variance in the dependent variable explained by the independent variable, but it does not directly indicate the size of the effect. The constant (D) represents the predicted value of the dependent variable when the independent variable is 0, but it does not show the size of the effect on the dependent variable.

Question 7

We run a simple regression using an independent variable X and a dependent variable Y. We find that there is absolutely no relationship between the two variables. What will the regression line look like?

Accepted Answer

When there is no relationship between the independent and dependent variables, the regression line will be a completely horizontal line at the mean of Y. This means that regardless of the value of X, the predicted value of Y will remain the same, which is the mean of Y.

Question 8

With simple regression, the best-fitting line is the one that:

Accepted Answer

The best-fitting line in simple regression is the one that has the least squared vertical distances from the points. This means that the line minimizes the sum of the squared vertical distances between the actual data points and the predicted values on the line. It is also known as the least squares regression line. The other choices are not correct because simply touching or having the least squared horizontal distances does not necessarily make the line the best-fitting one.

Question 9

Regular regression is also called OLS, or:

Accepted Answer

OLS stands for ordinary least squares regression, which is the most common type of regression analysis.

Question 10

With simple regression, if we want to know the strength of the relationship, the best statistic to look at is:

Accepted Answer

The best statistic to look at to determine the strength of the relationship with simple regression is the correlation coefficient (choice B). The correlation coefficient measures the strength and direction of the linear relationship between two variables. The slope (choice A) only tells us the direction of the relationship, while the constant (choice D) is simply a parameter in the regression equation. R-squared (choice C) can be helpful in determining the proportion of variance in the dependent variable that can be explained by the independent variable, but it does not provide information on the strength of the relationship.

Question 11

A researcher looks at two variables: the number of cats people own, and the number of dogs people own. She finds that the correlation coefficient is -.84. The best interpretation of this value is:

Accepted Answer

The negative correlation coefficient (-.84) indicates that as the number of dogs people own goes up, the number of cats people tend to own goes down. Option A and B are too specific and not necessarily true, and option D is too vague.

Question 12

With regard to positive signs and negative signs, which of the following is most accurate?

Accepted Answer

the formulas use the same numerator, and the denominator is always a positive value.

Question 13

A correlation coefficient of -.40 is ________ a correlation coefficient of +.40.

Accepted Answer

The strength of a correlation is determined by the absolute value of the correlation coefficient, not its sign. Both -.40 and +.40 have the same absolute value, indicating they are just as strong as each other, but in opposite directions.

Question 14

With simple regression, if we want to know the proportion of variation in the dependent variable that is explained by its relationship with the independent variable, the best statistic to look at is:

Accepted Answer

R-squared, often called the coefficient of determination, gives us the proportion of variation in the dependent variable that is explained by the independent variable. Therefore, it is the best statistic to look at if we want to know how much of the variation in the dependent variable can be attributed to the independent variable.

Question 15

In the movie gross forecasting example in the textbook, the removal of the James Cameron films from the sample:

Accepted Answer

Removing outliers or influential points like the high-grossing James Cameron films can often result in a stronger relationship between the variables being analyzed, as these outliers can skew the results and obscure the true nature of the relationship.

Question 16

The textbook suggests that if you're using a large number of cases and you end up with a small r-squared value of, say, 0.02, you should:

Accepted Answer

A low r-squared value does not necessarily indicate a problem with the data or analysis. Sometimes, the relationship between the variables being studied may simply be weak or non-existent. Therefore, it is best to be unphased and consider the limitations of the analysis.

Question 17

In the textbook example about health and work, which had the weakest correlation?

Accepted Answer

Women's missed work with women's emotional health had the weakest correlation, indicating that emotional health had less impact on their work attendance compared to other factors.

Question 18

In their article on U.S. politics, Healy and Lenz examine the correlation between:

Accepted Answer

Healy and Lenz focus on how economic growth impacts vote share, examining the idea that voters' perceptions of the economy significantly influence their voting behavior, often more so than campaign-specific factors.

Question 19

In Healy and Lenz's article on U.S. politics, they find __________ between economic growth and vote share.

Accepted Answer

Healy and Lenz's research in U.S. politics identifies a moderately strong correlation between economic growth and vote share, indicating that as the economy grows, incumbents tend to receive more votes.

Question 20

Jaeger uses which dataset in his study of physical attractiveness?

Accepted Answer

Jaeger used the Wisconsin Longitudinal Survey, which includes data on physical attractiveness and various other characteristics from a cohort of individuals in Wisconsin who graduated from high school in 1957.

Quiz 7: Give Me One Good Reason Why: Bivariate Correlation and Regression