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True/False Questions

Mod 3 Practice KEY

True/False

True The dependent variable is the variable that is being described, predicted, or controlled.
True A simple linear regression model is an equation that describes the straight-line relationship between a dependent variable and an independent variable.
True The residual is the difference between the observed value of the dependent variable and the predicted value of the dependent variable.
False When using simple regression analysis, if there is a strong correlation between the independent and dependent variable, then we can conclude that an increase in the value of the independent variable causes an increase in the value of the dependent variable.
True In a simple linear regression model, the correlation coefficient not only indicates the strength of the relationship between independent and dependent variable, but also shows whether the relationship is positive or negative.
True If r = -1, then we can conclude that there is a perfect relationship between X and Y.

True The slope of the simple linear regression equation represents the average change in the value of the dependent variable per unit change in the independent variable (X).

False The least squares simple linear regression line minimizes the sum of the vertical deviations between the line and the data points.

False The notation refers to the average value of the dependent variable Y.

False A significant positive correlation between X and Y implies that changes in X cause Y to change.

True The estimated simple linear regression equation minimizes the sum of the squared deviations between each value of Y and the line.

Multiple Choice

12. In a simple linear regression analysis, the correlation coefficient ( ) and the slope (m) _____ have the same sign.

A) always

B) sometimes

C) never

13. ________measures the strength of the linear relationship between the dependent and the independent variable.

A) Correlation coefficient

B) Distance value

C) Y Intercept

D) Residual

14. The least squares regression line minimizes the sum of the _______.

A) Differences between actual and predicted Y values

B) Absolute deviations between actual and predicted Y values

C) Absolute deviations between actual and predicted X values

D) Squared differences between actual and predicted Y values

E) Squared differences between actual and predicted X values

15. In simple regression analysis the quantity that gives the amount by which Y (dependent variable) changes for a unit change in X (independent variable) is called the

A) Coefficient of determination

B) Slope of the regression line

C) Y intercept of the regression line

D) Correlation coefficient

E) Standard error

16. The correlation coefficient may assume any value between

A) 0 and 1

B) - and 

C) 0 and 8

D) -1, and 1

E) -1, and 0

17. In simple regression analysis, if the correlation coefficient is a positive value, then

A) The Y intercept must also be a positive value.

B) The least squares regression equation could either have a positive or a negative slope.

C) The slope of the regression line must also be positive.

D) The standard error of estimate can either have a positive or a negative value.

18. The strength of the relationship between two quantitative variables can be measured by the:

A) slope of a simple linear regression equation

B) Y intercept of the simple linear regression equation

C) coefficient of correlation

19. After plotting the data points on a scatter diagram, we have the relationship to be falling to the right between the independent variable (X) and the dependent variable (Y). Therefore, we can expect both the sample _____ and the sample _____________ to be negative values.

A) Intercept, slope

B) Slope, SSE

C) Intercept, correlation coefficient

D) Slope, correlation coefficient

E) Slope, standard error of estimate

Fill-in-the-Blank

20. While the range for r² is between 0 and 1, the range for r is between

-1 and 1

21. The y intercept of the simple linear regression model is the value of y when the mean value of x is zero.

22. The least squares point estimates of the simple linear regression model minimize the SSE (sum of the squared errors).

23. Linear Regression Analysis is a statistical technique in which we use observed data to relate a dependent variable to one or more predictor (independent) variables.

24. The simple linear regression model assumes there is a linear relationship between the dependent variable and the independent variable.

25. In a simple linear regression model, the y intercept term is the mean value of y when x equals 0.

26. In a simple linear regression model, the slope term is the change in the mean value of y associated with a 1 unit increase in x.

27. The Correlation coefficient measures the strength of the relationship between a dependent variable (Y) and an independent variable (X). It is a unit less measure, therefore does not have an interpretative connotation, as does the coefficient of determination, .

28. After plotting the data points on a scatter diagram, we have observed an inverse relationship between the independent variable (X) and the dependent variable (Y). Therefore, we can expect both the sample slope and the sample Correlation coefficient to be a negative value.

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