Exam 13: Multiple Regression and Correlation Analysis

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 levelof education attained. [Adapted from 1^st Canadian Lind text 14-14] 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?

Twenty-one executives in a large corporation were randomly selected for a study in which several factors were examined to determine their effect on annual salary (expressed in $000's). The factors selected were age, seniority, years of college, number of company divisions they had been exposed to and the level of their responsibility. A regression analysis was performed using a popular spreadsheet program with the following regression output: -What is the effect on salary of an increase in age of two years if other variables are held constant?____________

i. The multiple standard error of estimate for two independent variables measures the variation about a regression plane. Ii) A multiple correlation determination equalling -0.76 is definitely possible. Iii) Multiple R² measures the proportion of explained variation relative to total variation.

If the coefficient of multiple determination is 0.81, what percent of variation is not explained?

Twenty-one executives in a large corporation were randomly selected for a study in which several factors were examined to determine their effect on annual salary (expressed in $000's). The factors selected were age, seniority, years of college, number of company divisions they had been exposed to and the level of their responsibility. A regression analysis was performed using a popular spreadsheet program with the following regression output: -Which of the following has the most influence on salary--20 years of seniority, 5 years of college or attaining 55 years of age?____________

i. A multiple regression equation defines the relationship between the dependent variable and the independent variables in the form of an equation. Ii) Autocorrelation often happens when data has been collected over periods of time. Iii) Homoscedasticity occurs when the variance of the residuals (Y - Y') is different for different values of Y'.

The production of automobile tires in any given year is related to the number of automobiles produced this year and in prior years. Suppose our econometric model resulted in the following data. -Which variable in the model is the most significant predictor of tire production?

The following correlations were computed as part of a multiple regression analysis that used education, job, and age to predict income. Which independent variable has the weakest association with the dependent variable?

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 Of education attained. Determine the regression equation.

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. -For which independent variable does a unit change have the greatest effect on the GPA? ____________

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.[Adapted from 1^st Canadian Lind text 14-14] Given the regression equation Poor (%) = -3.81 + 0.798 Single-Families (%) + 0.624 Unemployment Rate (%) - 0.170 Bachelor's Degree (%) - 0.003 High School (%) How many dependent variables are there in this regression?

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 0.05 level of significance?

A real estate agent developed a model to relate a house's selling price (Y) to the area of floor space (X) and the area of floor space squared (X2). The multiple regression equation for this model is: Y = 125 - 3X + X2 where: Y = selling price (times $1,000) X = square feet of floor space (times 100) -What is the selling price of a house with 1,500 square feet?____________

i. Violating the need for successive observations of the dependent variable to be uncorrelated is called autocorrelation. Ii) If an inverse relationship exists between the dependent variable and independent variables, the regression coefficients for the independent variables are negative. Iii) Given a multiple linear equation Y' = 5.1 + 2.2X1 - 3.5X2, assuming other things are held constant, an increase in one unit of the second independent variable will cause a -3.5 unit change in Y.

A real estate agent developed a model to relate a house's selling price (Y) to the area of floor space (X) and the area of floor space squared (X2). The multiple regression equation for this model is: Y = 125 - 3X + X2 where: Y = selling price (times $1,000) X = square feet of floor space (times 100) -What is the intercept (a)?____________

What are the degrees of freedom associated with the regression sum of squares?

In multiple regression, a dummy variable can be included in a multiple regression model as

What test investigates whether all the independent variables have zero net regression coefficients?

A real estate agent developed a model to relate a house's selling price (Y) to the area of floor space (X) and the area of floor space squared (X2). The multiple regression equation for this model is: Y = 125 - 3X + X2 where: Y = selling price (times $1,000) X = square feet of floor space (times 100) -What is the selling price of a house with 2,000 square feet?____________

A manager at a local bank analyzed the relationship between monthly salary and three independent variables: length of service (measured in months), gender (0 = female, 1 = male) and job type (0 = Clerical, 1 = technical). The following ANOVA summarizes the regression results: The results for the variable gender show that