Question 1

Regression analysis can be applied equally well to cross-sectional and time series data.

Accepted Answer

Regression analysis can be used to analyze both cross-sectional and time series data. Cross-sectional data involves analyzing data at a single point in time for multiple individuals or entities, while time series data involves analyzing data over multiple points in time for a single individual or entity. Regression analysis can help identify relationships between different variables and provide insights into predictive modeling for both types of data.

Question 2

In a simple linear regression problem,if the percentage of variation explained $R ^ { 2 }$ 
is 0.95,this means that 95% of the variation in the explanatory variable X can be explained by regression.

Accepted Answer

In a simple linear regression, $R^2$ indicates the percentage of variation in the dependent variable Y that is explained by the independent variable X, not the other way around.

Question 3

A regression analysis between weight (Y in pounds)and height (X in inches)resulted in the following least squares line: $\hat { y }$ 
= 140 + 5X.This implies that if the height is increased by 1 inch,the weight is expected to increase on average by 5 pounds.

Accepted Answer

The coefficient of X in the regression equation (5) represents the average change in Y (weight) for a one-unit increase in X (height).

Question 4

In every regression study there is a single variable that we are trying to explain or predict.This is called the response variable or dependent variable.

Accepted Answer

In a regression study, the response variable or dependent variable is the variable that is being explained or predicted. It is the variable that we are interested in studying and analyzing relationships with other variables.

Question 5

The effect of a logarithmic transformation on a variable that is skewed to the right by a few large values is to "squeeze" the values together and make the distribution more symmetric

Accepted Answer

This is true because the logarithmic transformation compresses the larger values, which then spreads out the smaller values to create a more symmetric distribution.

Question 6

In a simple regression with a single explanatory variable,the multiple R is the same as the standard correlation between the Y variable and the explanatory X variable.

Accepted Answer

The answer of In a simple regression with a single...

Question 7

Correlation is used to determine the strength of the linear relationship between an explanatory variable X and response variable Y.

Accepted Answer

Correlation measures the strength and direction of a linear relationship between two variables.

Question 8

In a nonlinear transformation of data,the Y variable or the X variables may be transformed,but not both.

Accepted Answer

Both the Y variable and the X variables may be transformed in a nonlinear transformation of data.

Question 9

In simple linear regression,the divisor of the standard error of estimate $S _ { e }$ 
is n - 1;simply because there is only one explanatory variable of interest.

Accepted Answer

In simple linear regression, the divisor for the standard error of estimate $S_e$ is $n - 2$ because two parameters (the intercept and the slope) are estimated from the data.

Question 10

The adjusted R² is used primarily to monitor whether extra explanatory variables really belong in a multiple regression model

Accepted Answer

The adjusted R², also known as the adjusted R-squared, is a measure of how well a multiple regression model fits the data. It takes into account the number of independent variables in the model, and adjusts the R-squared value accordingly. It is used primarily to assess the goodness of fit of a model, and to determine whether adding more explanatory variables to the model improves the fit significantly. Therefore, the statement that it is used to monitor whether extra explanatory variables really belong in a multiple regression model is true.

Question 11

Cross-sectional data are usually data gathered from approximately the same period of time from a cross-sectional of a population.

Accepted Answer

Cross-sectional data are indeed gathered from a cross-sectional of a population during approximately the same period of time. This type of data collection differs from longitudinal data, which gathers information over a longer period of time from the same individuals or groups.

Question 12

When the scatterplot appears as a shapeless swarm of points,this can indicate that there is no relationship between the response variable Y and the explanatory variable X,or at least none worth pursuing.

Accepted Answer

When the scatterplot appears as a shapeless swarm of points, it usually indicates that there is no discernible pattern or relationship between the response variable Y and the explanatory variable X. Therefore, pursuing a relationship between the two variables may not be worthwhile.

Question 13

The residual is defined as the difference between the actual and predicted,or fitted values of the response variable.

Accepted Answer

This is the correct definition of a residual.

Question 14

In a multiple regression problem with two explanatory variables if,the fitted regression equation is $\hat { Y } = 56.6 - 4.5 X _ { 1 } + 0.60 X _ { 2 } \text {, then the estimated value of } Y \text { when } X _ { 1 } = 2 \text { and } X _ { 2 } = 3 \text { is } 49.4$ 
.

Accepted Answer

The estimated value of Y is calculated by plugging the values of X1 and X2 into the fitted regression equation:$\hat { Y } = 56.6 - 4.5 X _ { 1 } + 0.60 X _ { 2 } $$\hat { Y } = 56.6 - 4.5 (2) + 0.60 (3) $$\hat { Y } = 56.6 - 9 + 1.8 $$\hat { Y } = 49.4 $

Question 15

For the multiple regression model $\bar { Y } = 40 + 15 X _ { 1 } - 10 X _ { 2 } + 5 X _ { 3 }$ 
,if $X _ { 2 }$ 
were to increase by 5 units,holding $X _ { 1 }$ 
and $X _ { 3 }$ 
constant,the value of Y would be expected to decrease by 50 units.

Accepted Answer

The coefficient of $X_2$ is -10, so an increase of 5 units in $X_2$ would result in a change of $-10 \times 5 = -50$ in $\bar{Y}$.

Question 16

A regression analysis between sales (in $1000)and advertising (in $100)resulted in the following least squares line: $$\hat { Y }$$ 
= 84 +7X.This implies that if advertising is $800,then the predicted amount of sales (in dollars)is $140,000.

Accepted Answer

The predicted amount of sales is $140,000 when advertising is $800, which is equal to 84 + 7(8) = 140.

Question 17

The regression line $$\hat { Y }$$ 
= 3 + 2X has been fitted to the data points (4,14), (2,7),and (1,4).The sum of the residuals squared will be 8.0.

Accepted Answer

The sum of the squared residuals is calculated by finding the difference between the actual and predicted values for each data point, squaring those differences, and summing them. For the given data points, this sum is not 8.0.

Question 18

In a simple regression analysis,if the standard error of estimate $s _ { e }$ 
= 15 and the number of observations n = 10,then the sum of the residuals squared must be 120.

Accepted Answer

The sum of the residuals squared is calculated as $s_e^2 \times (n - 2)$. With $s_e = 15$ and $n = 10$, it should be $15^2 \times (10 - 2) = 1800$, not 120.

Question 19

To help explain or predict the response variable in every regression study,we use one or more explanatory variables.These variables are also called response variables or independent variables.

Accepted Answer

Explanatory variables are also known as independent variables, not response variables. Response variables are the outcomes we are trying to predict or explain.

Question 20

A constant elasticity,or multiplicative,model the dependent variable is expressed as a product of explanatory variables raised to powers

Accepted Answer

In a constant elasticity or multiplicative model, the dependent variable is expressed as a product of explanatory variables raised to powers, which is a form of multiplicative relationship between the variables. Therefore, the statement is true.

Quiz 10: Regression Analysis: Estimating Relationships

Regression analysis can be applied equally well to cross-sectional and time series data.

In a simple linear regression problem,if the percentage of variation explained $R ^ { 2 }$ is 0.95,this means that 95% of the variation in the explanatory variable X can be explained by regression.

A regression analysis between weight (Y in pounds)and height (X in inches)resulted in the following least squares line: $\hat { y }$ = 140 + 5X.This implies that if the height is increased by 1 inch,the weight is expected to increase on average by 5 pounds.

In every regression study there is a single variable that we are trying to explain or predict.This is called the response variable or dependent variable.

The effect of a logarithmic transformation on a variable that is skewed to the right by a few large values is to "squeeze" the values together and make the distribution more symmetric

In a simple regression with a single explanatory variable,the multiple R is the same as the standard correlation between the Y variable and the explanatory X variable.

Correlation is used to determine the strength of the linear relationship between an explanatory variable X and response variable Y.

In a nonlinear transformation of data,the Y variable or the X variables may be transformed,but not both.

In simple linear regression,the divisor of the standard error of estimate $S _ { e }$ is n - 1;simply because there is only one explanatory variable of interest.

The adjusted R² is used primarily to monitor whether extra explanatory variables really belong in a multiple regression model

Cross-sectional data are usually data gathered from approximately the same period of time from a cross-sectional of a population.

When the scatterplot appears as a shapeless swarm of points,this can indicate that there is no relationship between the response variable Y and the explanatory variable X,or at least none worth pursuing.

The residual is defined as the difference between the actual and predicted,or fitted values of the response variable.

In a multiple regression problem with two explanatory variables if,the fitted regression equation is $\hat { Y } = 56.6 - 4.5 X _ { 1 } + 0.60 X _ { 2 } \text {, then the estimated value of } Y \text { when } X _ { 1 } = 2 \text { and } X _ { 2 } = 3 \text { is } 49.4$ .

For the multiple regression model $\bar { Y } = 40 + 15 X _ { 1 } - 10 X _ { 2 } + 5 X _ { 3 }$ ,if $X _ { 2 }$ were to increase by 5 units,holding $X _ { 1 }$ and $X _ { 3 }$ constant,the value of Y would be expected to decrease by 50 units.

A regression analysis between sales (in $1000)and advertising (in $100)resulted in the following least squares line: $\hat { Y }$ = 84 +7X.This implies that if advertising is $800,then the predicted amount of sales (in dollars)is $140,000.

The regression line $\hat { Y }$ = 3 + 2X has been fitted to the data points (4,14), (2,7),and (1,4).The sum of the residuals squared will be 8.0.

In a simple regression analysis,if the standard error of estimate $s _ { e }$ = 15 and the number of observations n = 10,then the sum of the residuals squared must be 120.

To help explain or predict the response variable in every regression study,we use one or more explanatory variables.These variables are also called response variables or independent variables.

A constant elasticity,or multiplicative,model the dependent variable is expressed as a product of explanatory variables raised to powers

Quiz 10: Regression Analysis: Estimating Relationships

Regression analysis can be applied equally well to cross-sectional and time series data.

In a simple linear regression problem,if the percentage of variation explained R2R ^ { 2 }R2 is 0.95,this means that 95% of the variation in the explanatory variable X can be explained by regression.

A regression analysis between weight (Y in pounds)and height (X in inches)resulted in the following least squares line: y^\hat { y }y^​ = 140 + 5X.This implies that if the height is increased by 1 inch,the weight is expected to increase on average by 5 pounds.

In every regression study there is a single variable that we are trying to explain or predict.This is called the response variable or dependent variable.

The effect of a logarithmic transformation on a variable that is skewed to the right by a few large values is to "squeeze" the values together and make the distribution more symmetric

In a simple regression with a single explanatory variable,the multiple R is the same as the standard correlation between the Y variable and the explanatory X variable.

Correlation is used to determine the strength of the linear relationship between an explanatory variable X and response variable Y.

In a nonlinear transformation of data,the Y variable or the X variables may be transformed,but not both.

In simple linear regression,the divisor of the standard error of estimate SeS _ { e }Se​ is n - 1;simply because there is only one explanatory variable of interest.

The adjusted R2 is used primarily to monitor whether extra explanatory variables really belong in a multiple regression model

Cross-sectional data are usually data gathered from approximately the same period of time from a cross-sectional of a population.

When the scatterplot appears as a shapeless swarm of points,this can indicate that there is no relationship between the response variable Y and the explanatory variable X,or at least none worth pursuing.

The residual is defined as the difference between the actual and predicted,or fitted values of the response variable.

A regression analysis between sales (in $1000)and advertising (in $100)resulted in the following least squares line: Y^\hat { Y }Y^ = 84 +7X.This implies that if advertising is $800,then the predicted amount of sales (in dollars)is $140,000.

The regression line Y^\hat { Y }Y^ = 3 + 2X has been fitted to the data points (4,14), (2,7),and (1,4).The sum of the residuals squared will be 8.0.

In a simple regression analysis,if the standard error of estimate ses _ { e }se​ = 15 and the number of observations n = 10,then the sum of the residuals squared must be 120.

To help explain or predict the response variable in every regression study,we use one or more explanatory variables.These variables are also called response variables or independent variables.

A constant elasticity,or multiplicative,model the dependent variable is expressed as a product of explanatory variables raised to powers

In a simple linear regression problem,if the percentage of variation explained $R ^ { 2 }$ is 0.95,this means that 95% of the variation in the explanatory variable X can be explained by regression.

A regression analysis between weight (Y in pounds)and height (X in inches)resulted in the following least squares line: $\hat { y }$ = 140 + 5X.This implies that if the height is increased by 1 inch,the weight is expected to increase on average by 5 pounds.

In simple linear regression,the divisor of the standard error of estimate $S _ { e }$ is n - 1;simply because there is only one explanatory variable of interest.

The adjusted R² is used primarily to monitor whether extra explanatory variables really belong in a multiple regression model

A regression analysis between sales (in $1000)and advertising (in $100)resulted in the following least squares line: $\hat { Y }$ = 84 +7X.This implies that if advertising is $800,then the predicted amount of sales (in dollars)is $140,000.

The regression line $\hat { Y }$ = 3 + 2X has been fitted to the data points (4,14), (2,7),and (1,4).The sum of the residuals squared will be 8.0.

In a simple regression analysis,if the standard error of estimate $s _ { e }$ = 15 and the number of observations n = 10,then the sum of the residuals squared must be 120.