Exam 12: Multiple Regression and Model Building

A researcher in human resources has expressed concern about the differences in job satisfaction results across units within an organization. The researcher conducts a study to investigate what factors could account for the differences. The researcher looked at a random sample of units across the organization and used the factors of percentage of employees with a university degree, the average age of the employees, and the average salary of employees within a unit. The results of the study are presented below: Predictor Coef SE Coef Constant 35.178 7.595 Degree 0.22073 0.07131 Age 0.3353 0.1901 Salary 0.0930 0.1675 $s = 7.62090$ Analysis of Variance Source DF SS Regression 3 1053.09 Residual Error 32 1858.50 Source DF Seq SS Degree 1 672.10 Age 1 363.09 Salary 1 17.90 -Using the results above,what is the explained variation?

Below is a partial multiple regression computer output based on a quadratic regression model. Source SS df Model 29.44 2 Error 59.96 15 Standard Error Variable Coefficient Intercept 8.01 1.45 -1.35 0.55 0.46 0.43 -Calculate R².

Below is a partial multiple regression computer output based on a quadratic regression model to predict student enrollment at a local university.The dependent variable is the annual enrolment given in thousands of students,the independent variable X is the increase in tuition stated in thousands of dollars per year,and X² is the square of tuition increase given in squared thousands of dollars per year. Interpret β₀(the y intercept)and β₁(the β coefficient for the X variable).Does the parabola open upward or downward? Why?

Testing the contribution of individual independent variables with t-tests is performed prior to the F-test for the model in multiple regression analysis.

The graph of the prediction equation obtained from fitting the model $\mathrm { y } = \beta _ { 0 } + \beta _ { 1 } X _ { 1 } + \beta _ { 2 } X _ { 2 } + \varepsilon$ Is a(n):

Consider the following partial computer output for a multiple regression model. Predictor Coefficient Standard Deviation Constant 41.225 6.380 1.081 1.353 -18.404 4.547 Analysis of Variance Source Regression 2 2270.11 Error (residual) 26 3585.75 -What is the number of observations in the sample?

The management of a professional baseball team is in the process of determining the budget for next year.A major component of future revenue is attendance at the home games.In order to predict attendance at home games,the team's statistician has used a multiple regression model with dummy variables.The model is of the form: y = β₀+ β₁x₁+ β₂x₂+ β₃x₃+ ε where: Y = attendance at a home game x1= current power rating of the team on a scale from 0 to 100 before the game. x2and x3are dummy variables,and they are defined below. x2= 1,if weekend x2= 0,otherwise x3= 1,if weather is favourable x3= 0,otherwise After collecting the data based on 30 games from last year and implementing the above stated multiple regression model,the team statistician obtained the following least squares multiple regression equation: $\hat { y } = - 1050 + 250 x _ { 1 } + 2200 x _ { 2 } + 5400 x _ { 3 }$ The multiple regression compute output also indicated the following: $s _ { b _ { 1 } } = 800 , s _ { b _ { 2 } } = 1000 , s _ { b _ { 3 } } = 1850$ -Assume that the overall model is useful in predicting the game attendance.Assume today is Wednesday morning and the weather forecast indicates sunny,excellent weather conditions for the rest of the day.Later today,there is a home baseball game for this team.Assume that the current power rating of the team is 85 and predict the attendance for today's game.

A member of the provincial legislature has expressed concern about the differences in the mathematics test scores of grade 9 high school students across the province.She asks her research assistant to conduct a study to investigate what factors could account for the differences.The research assistant looked at a random sample of school districts across the province and used the factors of percentage of mathematics teachers in each district with a degree in mathematics,the average age of mathematics teachers,and the average salary of mathematics teachers Predictor Coef SE Coef Constant 35.178 7.595 Math Dgr 0.22073 0.07131 Age 0.3353 0.1901 Salary 0.0930 0.1675 s = 7.62090 Analysis of Variance Source DF SS Regression 3 1053.09 Residual Error 32 1858.50 Source DF Seq SS Math Dgr 1 672.10 Age 1 363.09 Salary 1 17.90 -What is the number of observations in the sample?

A member of the provincial legislature has expressed concern about the differences in the mathematics test scores of grade 9 high school students across the province.She asks her research assistant to conduct a study to investigate what factors could account for the differences.The research assistant looked at a random sample of school districts across the province and used the factors of percentage of mathematics teachers in each district with a degree in mathematics,the average age of mathematics teachers,and the average salary of mathematics teachers Predictor Coef SE Coef Constant 35.178 7.595 Math Dgr 0.22073 0.07131 Age 0.3353 0.1901 Salary 0.0930 0.1675 s = 7.62090 Analysis of Variance Source DF SS Regression 3 1053.09 Residual Error 32 1858.50 Source DF Seq SS Math Dgr 1 672.10 Age 1 363.09 Salary 1 17.90 -What is the explained variation?

The difference between the observed values of y and the predicted value of y is referred to as a(n)_____.

In multiple regression analysis,[explained variation/(k+1)]/MSE yields the:

Below is a partial multiple regression computer output. Source SS df Model 32,774 5 Error 21,886 292 Total 54,660 297 -What is the value of the F statistic?

Even when an unimportant variable is added to a regression model,the explained variation will increase.

The effects of different levels of qualitative independent variables are described using _____ variables.

In multiple regression analysis,which one of the following is the appropriate notation for error (residual)?

Consider the following partial computer output for a multiple regression model. Predictor Coefficient Standard Dev Constant 99.3883 1 -0.007207 0.0031 2 0.0011336 0.00122 3 0.9324 0.373 Analysis of Variance Source 31.308 Regression 3 9.378 Error (residual) 16 -What is the value of F?

In using a regression model,if a new independent variable is added,the value of the R²(coefficient of multiple determination)will ___________ decrease.

A member of the provincial legislature has expressed concern about the differences in the mathematics test scores of grade 9 high school students across the province.She asks her research assistant to conduct a study to investigate what factors could account for the differences.The research assistant looked at a random sample of school districts across the province and used the factors of percentage of mathematics teachers in each district with a degree in mathematics,the average age of mathematics teachers,and the average salary of mathematics teachers Predictor Coef SE Coef Constant 35.178 7.595 Math Dgr 0.22073 0.07131 Age 0.3353 0.1901 Salary 0.0930 0.1675 s = 7.62090 Analysis of Variance Source DF SS Regression 3 1053.09 Residual Error 32 1858.50 Source DF Seq SS Math Dgr 1 672.10 Age 1 363.09 Salary 1 17.90 -What is the mean square error?

A multiple regress model is fit using five independent variables.A sixth independent variable is added from the data set and the model is refit.As a result,the value of explained variation (SSR)will _________,and the value of multiple coefficient of determination (R²)will _________.

Consider the following partial computer output for a multiple regression model. Predictor Coefficient Standard Dev Constant 99.3883 1 -0.007207 0.0031 2 0.0011336 0.00122 3 0.9324 0.373 Analysis of Variance Source 31.308 Regression 3 9.378 Error (residual) 16 -What is the explained variation?