Exam 12: Regression and Correlation

The best fitting line is one where the

What is the slope of the linear regression prediction equation if a person with 12 years of schooling earns $31,000 per year and a person with 13 years of schooling earns $32,500 per year?

A bivariate regression assumes that the variables have a linear or straight-line relationship.

The following data on fertility rates were obtained from Eurostat on seven European countries in 2006.Suppose you obtain the following equation which predicts the total fertility rate using information on the mean age of childbearing: Y = 9.34 - 0.25x.What is the predicted total fertility rate for a country with a mean age at childbearing of 31.5 years? Why would it be inappropriate to predict,say,the TFR for a country with a mean age at childbearing of 22.7 years?

The least-square method is a technique that chooses a and b such that the residual sum of squares is the least.

The following data on fertility rates were obtained from Eurostat on seven European countries in 2006.What is direction of the relationship between the mean age at childbearing and the total fertility rate? Which single country appears to be the exception?

Define Covariance (X,Y).

Consider the following linear regression prediction equation: Y = 12 + -1x.What is the direction of the relationship between these two variables?

The coefficient of determination is symbolized by

Which of the following would be the least squares (best fitting)line?

Residual sum of squares, $S S E=\sum(Y-\bar{Y})^{2}$ .

What role does the coefficient of determination play in regression?

The following data on fertility rates were obtained from Eurostat on seven European countries in 2006.Considering the total fertility rate as your dependent variable,construct a scatter diagram and plot the seven observations in the table.

The following data were obtained from a sample of 12 respondents.Suppose that we started by calculating a bivariate regression equation which predicted children's education using information on fathers' education.Suppose further that we then calculated a multiple regression equation which predicted children's education using information on both fathers' education and mothers' education.What would you expect to happen to the sum of squares regression in the multiple regression equation relative to the sum of squares regression in the bivariate linear regression equation? Does it increase or decrease in value? Why?

What does the quantity r refer to?

Consider the following linear regression prediction equation: Y = 12 + -1x.What is the direction of the relationship between these two variables?

Assume that a local company pays its employees 25 cents more per hour for each college credit earned during a given year.Consider two employees,one earning $10 per hour and having earned zero college credits and one earning $12 per hour and having earned eight college credits.What is the Y-intercept of the linear regression prediction equation?

Consider the following linear regression prediction equation: Y = 12 + -1x.If the predicted value of Y for an observation is 5,calculate the residual for an observation where the observed value of Y is equal to 9.

The following data were obtained from a sample of 12 respondents.In reviewing the above data,imagine that you first decide to calculate Pearson's correlation coefficient for the relationship between the highest grade of school completed for respondents and their fathers.If the covariance between respondents' and fathers' education is 3.23,what is the value of Pearson's correlation coefficient?

A scatter diagram is a visual method used to display a relationship between two ______ variables.