Question 1

In a study where the least squares estimates were based on 34 sets of sample observations, the total sum of squares and regression sum of squares were found to be: SST = 4.53 and SSR = 4.21. What is the error sum of squares?

Accepted Answer

The error sum of squares (SSE) is calculated by subtracting the regression sum of squares (SSR) from the total sum of squares (SST). Therefore, SSE = SST - SSR = 4.53 - 4.21 = 0.32.

Question 2

It is important to review residual plots to identify any signs of _____ and correlated observations in cross-sectional and time-series studies.

Accepted Answer

Changing variability in residual plots indicates that the variance of errors is not constant, which is an important assumption in many statistical models. Reviewing residual plots helps identify this issue, as well as correlated observations, which can affect the validity of the model.

Question 3

In Excel, to construct a residual plot, input of a y range and an x range is needed. Aimee is examining the relationship between age and square foot range (sqft) of living space. In the scenario provided, what would be the y and what would be the x range data?

Accepted Answer

The y range would be age because it is the dependent variable, and the x range would be sqft because it is the independent variable.

Question 4

Regression analysis captures the relationship between only two distinct variables.

Accepted Answer

Regression analysis can capture the relationship between one dependent variable and one or more independent variables, not limited to just two distinct variables.

Question 5

The response variable is the outcome of a variable, whereas the predictor is the input variable(s).

Accepted Answer

The response variable, also known as the dependent variable, is the outcome of interest that is being measured or predicted, while the predictor(s), or independent variable(s), are the input variables that are used to predict or explain changes in the response variable.

Question 6

Quantitative variables are numeric, whereas qualitative variables are descriptors reflecting categories.

Accepted Answer

Quantitative variables represent quantities and can be counted or measured, allowing for numerical operations. Qualitative variables, on the other hand, describe attributes or categories and cannot be measured in numbers but rather are used to classify or distinguish between different types.

Question 7

R²in linear regression is the correlation coefficient.

Accepted Answer

R² does not refer to any known standard notation in linear regression or statistics, and the correlation coefficient is typically denoted by "r" or "R" in the context of linear regression.

Question 8

Analysis of covariance (ANCOVA) is used in the context of linear regression to derive R².

Accepted Answer

Analysis of Covariance (ANCOVA) is primarily used to control for the effects of one or more covariate variables that are not of primary interest, in order to focus more accurately on the primary independent variable(s) of interest, rather than being used to derive specific components within linear regression.

Question 9

The total sum of squares (SST) can be broken into two: explained variation and unexplained variation.

Accepted Answer

The total sum of squares (SST) is indeed divided into two components: the sum of squares due to regression (SSR), which represents the explained variation, and the sum of squares due to error (SSE), which represents the unexplained variation.

Question 10

When using Excel for a one-tailed test, the returned p-value will need to be divided in half.

Accepted Answer

In Excel, when performing a one-tailed test using functions that typically return a p-value for a two-tailed test (like T.TEST), the returned p-value must be divided in half to get the correct p-value for the one-tailed test.

Question 11

When working with big data, a sample size is significantly large if the variability virtually disappears.

Accepted Answer

When working with big data, the variability of the data is often so small that it can be considered negligible. This means that a sample size that is large enough to represent the population will be significantly large enough to eliminate any variability.

Question 12

If the Ordinary Lease Squares (OLS) required assumptions of linear regression are met, OLS estimators of the regression coefficients $\beta$_j are unbiased.

Accepted Answer

When the assumptions of the Ordinary Least Squares (OLS) method are met, the OLS estimators of the regression coefficients are unbiased, meaning the expected value of the estimators equals the true parameter values.

Question 13

If residual plots exhibit strong nonlinear patterns, the inferences made by a linear regression model can be quite accurate.

Accepted Answer

Residual plots exhibiting strong nonlinear patterns suggest that the linear regression model does not adequately capture the relationship between the variables, leading to inaccurate inferences.

Quiz 6: Regression Analysis

In a study where the least squares estimates were based on 34 sets of sample observations, the total sum of squares and regression sum of squares were found to be: SST = 4.53 and SSR = 4.21. What is the error sum of squares?

It is important to review residual plots to identify any signs of _____ and correlated observations in cross-sectional and time-series studies.

In Excel, to construct a residual plot, input of a y range and an x range is needed. Aimee is examining the relationship between age and square foot range (sqft) of living space. In the scenario provided, what would be the y and what would be the x range data?

Regression analysis captures the relationship between only two distinct variables.

The response variable is the outcome of a variable, whereas the predictor is the input variable(s).

Quantitative variables are numeric, whereas qualitative variables are descriptors reflecting categories.

R²in linear regression is the correlation coefficient.

Analysis of covariance (ANCOVA) is used in the context of linear regression to derive R².

The total sum of squares (SST) can be broken into two: explained variation and unexplained variation.

When using Excel for a one-tailed test, the returned p-value will need to be divided in half.

When working with big data, a sample size is significantly large if the variability virtually disappears.

If the Ordinary Lease Squares (OLS) required assumptions of linear regression are met, OLS estimators of the regression coefficients $\beta$ _j are unbiased.

If residual plots exhibit strong nonlinear patterns, the inferences made by a linear regression model can be quite accurate.

Quiz 6: Regression Analysis

In a study where the least squares estimates were based on 34 sets of sample observations, the total sum of squares and regression sum of squares were found to be: SST = 4.53 and SSR = 4.21. What is the error sum of squares?

It is important to review residual plots to identify any signs of _____ and correlated observations in cross-sectional and time-series studies.

In Excel, to construct a residual plot, input of a y range and an x range is needed. Aimee is examining the relationship between age and square foot range (sqft) of living space. In the scenario provided, what would be the y and what would be the x range data?

Regression analysis captures the relationship between only two distinct variables.

The response variable is the outcome of a variable, whereas the predictor is the input variable(s).

Quantitative variables are numeric, whereas qualitative variables are descriptors reflecting categories.

R2 in linear regression is the correlation coefficient.

Analysis of covariance (ANCOVA) is used in the context of linear regression to derive R2.

The total sum of squares (SST) can be broken into two: explained variation and unexplained variation.

When using Excel for a one-tailed test, the returned p-value will need to be divided in half.

When working with big data, a sample size is significantly large if the variability virtually disappears.

If the Ordinary Lease Squares (OLS) required assumptions of linear regression are met, OLS estimators of the regression coefficients β\betaβ j are unbiased.

If residual plots exhibit strong nonlinear patterns, the inferences made by a linear regression model can be quite accurate.

R²in linear regression is the correlation coefficient.

Analysis of covariance (ANCOVA) is used in the context of linear regression to derive R².

If the Ordinary Lease Squares (OLS) required assumptions of linear regression are met, OLS estimators of the regression coefficients $\beta$ _j are unbiased.