Question 1

A measure of how well an estimated regression line fits the sample data on which it is based (denoted by  and equal to the proportion of the total variation in the values of the dependent variable, y, that can be explained by the association of y with x as measured by the estimated regression line) is called the sample coefficient of correlation.

Accepted Answer

The answer of A measure of how well an estimated...

Question 2

The standard error of the estimate in a simple linear regression model measures the variation in the slope coefficient from sample to sample.

Accepted Answer

The standard error of the estimate measures the variation in the dependent variable (y) around the regression line. It does not measure the variation in the slope coefficient from sample to sample.

Question 3

In developing a scatterplot, you have the option of connecting the points or not.

Accepted Answer

The answer of In developing a scatterplot, you have the...

Question 4

If a simple linear regression model is developed based on a sample where the independent and dependent variables are known to be positively related, then the sign of the slope regression coefficient will be positive also.

Accepted Answer

If two variables are known to be positively related, a change in the independent variable will result in a corresponding change in the dependent variable in the same direction. Therefore, a simple linear regression model developed between these variables will have a positive slope regression coefficient, indicating the same positive relationship between the two variables.

Question 5

In a simple linear regression model, if the independent and dependent variables are negatively linearly related, then the standard error of the estimate will also be negative.

Accepted Answer

The standard error of the estimate is always non-negative, regardless of the relationship between the independent and dependent variables. It represents the average distance between the predicted values and the actual values, and cannot be negative.

Question 6

The values of a and  found in the equation of the true regression line, E(y) =  , represent the line's y-intercept and slope, respectively, and are called true regression coefficients.

Accepted Answer

The statement correctly defines the concept of true regression coefficients.

Question 7

In developing a simple linear regression model, only one independent variable is used to explain the variation in a single dependent variable.

Accepted Answer

A simple linear regression model uses only one independent variable to explain the variation in a single dependent variable.

Question 8

A dependent variable is the variable that we wish to predict in a regression model.

Accepted Answer

This is the correct definition of a dependent variable in a regression model.

Question 9

A direct relationship is a relationship between any two variables, Y and X, such that the value of Y is uniquely determined whenever the value of X is specified (only Y exists for each X).

Accepted Answer

A direct relationship implies that as X increases, Y also increases (or decreases together in an inverse relationship), but it doesn't mean Y is uniquely determined by X. Multiple Y values can exist for a single X in various types of relationships, including direct ones.

Question 10

In a sample linear regression model, the slope coefficient  represents the average change in the independent variable x for a one unit change in the dependent variable y.

Accepted Answer

The slope coefficient (11eb6b9e_0612_9d0f_8d9d_fd14c7804302_TB8220_11) represents the average change in the dependent variable y for a one unit change in the independent variable x, not the other way around.

Question 11

The values of  and b found in the equation of the estimated regression line,  , represent the line's y-intercept and slope, respectively, and are called estimated regression coefficients.

Accepted Answer

The values of b (found in the equation of the estimated regression line) represents the line's slope and the value of 11eb6b9e_0612_4eea_8d9d_f5d4bbafa560_TB8220_00 represents the line's y-intercept. These are indeed the estimated regression coefficients.

Question 12

In a simple linear regression model, if the regression model is statistically significant, then the regression slope coefficient is significantly greater than zero.

Accepted Answer

A statistically significant regression model indicates that the slope coefficient is significantly different from zero, but it does not specify whether the slope is greater than or less than zero.

Question 13

In regression analysis, the so-called regression line summarizes the stochastic relationship between dependent variable y and independent x, while also minimizing the errors made when the equation of that line is employed to estimate y from x.

Accepted Answer

This statement correctly describes the purpose and function of the regression line in regression analysis.

Question 14

A stochastic relationship is a relationship between any two variables, Y and X, such that many possible values of Y can be associated with any one value of X.

Accepted Answer

A stochastic relationship is also known as a probabilistic or statistical relationship, and it means that there is no fixed or deterministic equation that can perfectly predict the value of Y for a given value of X. Instead, Y is influenced by various random factors or uncertainties, leading to a range of possible outcomes.

Question 15

If two variables are related in a negative linear manner, the scatterplot will show points on the x, y space that are generally moving from the upper left to the lower right.

Accepted Answer

This is because as one variable increases, the other variable decreases, resulting in a negative correlation. The scatterplot will show a downward sloping line or pattern.

Question 16

If a set of data contains no values of the independent variable x that are equal to zero, then the y-intercept regression coefficient  has no particular meaning.

Accepted Answer

The y-intercept regression coefficient represents the predicted value of y when x is equal to zero. If there are no values of x equal to zero, then the coefficient has no practical meaning.

Question 17

An automobile company in Michigan is interested in the relationship between the gender of their employees and employee productivity. A good starting point in this analysis would be to compute the coefficient of determination and the correlation coefficient.

Accepted Answer

While the correlation coefficient may provide information on the strength and direction of the relationship between gender and productivity, it cannot determine causation or the degree to which one variable influences the other. Additionally, the coefficient of determination is a measure of how well a regression model fits the data, and may not be applicable in this scenario without additional information on the variables being analyzed. Other statistical methods, such as t-tests, ANOVA, or regression analysis, may be more suitable for exploring the relationship between gender and productivity in this context.

Question 18

In regression analysis, the dependent variable is a variable whose value is unknown and is being explained or predicted with the help of another variable.

Accepted Answer

In regression analysis, the dependent variable is indeed the variable being explained or predicted with the help of another variable, which is the independent variable.

Question 19

If a simple linear regression model is developed based on a sample where the independent and dependent variables are known to be negatively related, then the sum of squares for error will be negative also.

Accepted Answer

The sum of squares for error cannot be negative by definition. It is the sum of the squared differences between the actual values and the predicted values, and these differences cannot be negative. If the regression model is developed based on a sample where the independent and dependent variables are known to be negatively related, then the slope coefficient of the regression line will be negative and the sum of squares for error will be positive.

Question 20

The sign of the correlation coefficient in a simple linear regression model will always be the same as the sign of the y-intercept coefficient  .

Accepted Answer

The answer of The sign of the correlation coefficient in...

Quiz 12: Linear Regression and Correlation