Exam 13: Linear Regression and Correlation

It has been hypothesized that overall academic success for freshmen at college as measured by Grade point average (GPA) is a function of IQ scores (X1), hours spent studying each week (X2), and One's high school average (X3). Suppose the regression equation is: Y' = -6.9 + 0.055X1 + 0.107X2 + 0.0083X3. The multiple standard error is 6.313 and R2 = 0.826.What will the GPA be if the number of hours Spent studying is 30 the IQ is 108, and the high school average is 82?

Angela Chou has been asked to investigate the determinants of poverty in Ontario communities. She collected data on 60 communities from Statistics Canada. She selected the percentage of poor Persons living under the poverty line [Poor (%)], measured by Low Income Cut-Off, designed by Statistics Canada as a measure of poverty for a community, as the dependent variable. The Independent variables selected are percent of single families in each community, the Unemployment rate in each community, percent of population in the community holding a bachelor's Degree as their highest level of education attained, and percent of population holding a High School Diploma as their highest level of education attained. Given the regression equation Poor (%) = -3.81 + 0.798 Single-Families (%) + 0.624 Unemployment Rate (%) - 0.170 Bachelor's Degree (%) - 0.003 High School (%).- What is the estimated percentage of poor persons living below the poverty line in a community with 5% of the community as single-families, a 5% unemployment rate, only 5% holding a Bachelor's Degree and 25% having High School as their highest attained educational level?

In regression analysis, the dferr = ________.

What is the difference in selling prices of a house with 1,700 square feet and one with 1,800 square Feet?

The information below is from the multiple regression analysis computer output for 28 teams in Major League Baseball. The model is designed to predict wins using attendance, payroll, batting Average, home runs, stolen bases, errors, and team ERA. The t-value computed for testing the coefficient "Batg. Avg." is:

i. Multiple regression is used when two or more independent variables are used to predict a value Of a single dependent variable. ii. The values of b1, b2 and b3 in a multiple regression equation are called the net regression Coefficients. They indicate the change in the predicted value for a unit change in one X when the Other X variables are held constant. iii. Autocorrelation often happens when data has been collected over periods of time.

i. Multiple R2 measures the proportion of explained variation. ii. 90% of total variation in the dependent variable is explained by the independent variable for a Multiple R2= 0.90. iii. The multiple standard error of estimate measures the variation about the regression plane when Two independent variables are considered.

i. Multiple regression analysis examines the relationship of several dependent variables on the Independent variable. ii. A multiple regression equation defines the relationship between the dependent variable and the Independent variables in the form of an equation. iii. Autocorrelation often happens when data has been collected over periods of time.

Which of the following is a characteristic of the F-distribution?

Which variable in the model is the most significant predictor of tire production?

The following summary is from home heating costs, using mean outside temperature as X1 the Number of centimetres of insulation as X2, and the presence of a garage as X3. Is the presence of the independent variable garage significant in predicting heating costs, when Tested at the 0.01 level of significance?

The best example of an alternate hypothesis for a global test of a multiple regression model is:

The information below is from the multiple regression analysis computer output for 28 teams in Major League Baseball. The model is designed to predict wins using attendance, payroll, batting Average, home runs, stolen bases, errors, and team ERA. The critical value of F to be used in the global test of the model is: (5% level of significance)

What is the range of values for multiple R?

Angela Chou has been asked to investigate the determinants of poverty in Ontario communities. She collected data on 60 communities from Statistics Canada. She selected the percentage of poor Persons living under the poverty line [Poor (%)], measured by Low Income Cut-Off, designed by Statistics Canada as a measure of poverty for a community, as the dependent variable. The Independent variables selected are percent of single families in each community, the Unemployment rate in each community, and percent of population in the community holding a Bachelor's degree as their highest level of education attained. Determine the regression equation.

Hypotheses concerning individual regression coefficients are tested using which statistic?

In a multiple regression analysis, the following correlation matrix was computed. Which independent variable(s) are highly correlated with the dependent variable?

What is the effect on salary for an increase of one level of responsibility if the other variables are Held constant?

A sample of General Mills employees was studied to determine their degree of satisfaction with Their present life. A special index, called the index of satisfaction, was used to measure satisfaction. Six factors were studied: age at the time of first marriage (X1), annual income (X2), number of Children living (X3), value of all assets (X4), status of health in the form of an index (X5), and the Average number of social activities per week (X6). Suppose the multiple regression equation is: Y' = 16.24 + 0.017X1 + 0.00028X2 + 42X3 + 0.0012X4 + 0.09X5 + 26.8X6. Explain the meaning of b2.

The following graph is used to evaluate two assumptions of a multiple regression analysis. What are The two assumptions?