Exam 15: Multiple Regression

SCENARIO 15-7-B You are the CEO of a dairy company. You are planning to expand milk production by purchasing additional cows, lands and hiring more workers. From the existing 50 farms owned by the company, you have collected data on total milk production (in liters), the number of milking cows, land size (in acres) and the number of laborers. The data are shown below and also available in the Excel file Scenario15-7-DataB.XLSX. You believe that the number of milking cows $\left( X _ { 1 } \right)$ , land size $\left( X _ { 2 } \right)$ and the number of laborers $\left( X _ { 3 } \right)$ are the best predictors for total milk production on any given farm. -Referring to Scenario 15-7-B, the variable X1 should be dropped to remove collinearity?

SCENARIO 15-7-A You are the CEO of a dairy company. You are planning to expand milk production by purchasing additional cows, lands and hiring more workers. From the existing 50 farms owned by the company, you have collected data on total milk production (in liters), the number of milking cows, land size (in acres) and the number of laborers. The data are shown below and also available in the Excel file Scenario15-7-DataA.XLSX. You believe that the number of milking cows $\left( X _ { 1 } \right)$ , land size $\left( X _ { 2 } \right)$ and the number of laborers $\left( X _ { 3 } \right)$ are the best predictors for total milk production on any given farm. -Referring to Scenario 15-7-A, the p value of the t test statistic for testing whether the quadratic term for land size is statistically significant after you have performed a multiple regression that includes the quadratic terms for the number of milking cows, land size and the number of laborers is _____.

SCENARIO 15-7-B You are the CEO of a dairy company. You are planning to expand milk production by purchasing additional cows, lands and hiring more workers. From the existing 50 farms owned by the company, you have collected data on total milk production (in liters), the number of milking cows, land size (in acres) and the number of laborers. The data are shown below and also available in the Excel file Scenario15-7-DataB.XLSX. You believe that the number of milking cows $\left( X _ { 1 } \right)$ , land size $\left( X _ { 2 } \right)$ and the number of laborers $\left( X _ { 3 } \right)$ are the best predictors for total milk production on any given farm. -Referring to Scenario 15-7-B, the model that includes only $X _ { 1 } \text { and } X _ { 3 }$ should be among the appropriate models using the Mallow's Cp statistic.

SCENARIO 15-7-A You are the CEO of a dairy company. You are planning to expand milk production by purchasing additional cows, lands and hiring more workers. From the existing 50 farms owned by the company, you have collected data on total milk production (in liters), the number of milking cows, land size (in acres) and the number of laborers. The data are shown below and also available in the Excel file Scenario15-7-DataA.XLSX. You believe that the number of milking cows $\left( X _ { 1 } \right)$ , land size $\left( X _ { 2 } \right)$ and the number of laborers $\left( X _ { 3 } \right)$ are the best predictors for total milk production on any given farm. -Referring to Scenario 15-7-A, the value of the t test statistic for testing whether the quadratic term for land size is statistically significant after you have performed a multiple regression that includes the quadratic terms for the number of milking cows, land size and the number of laborers is _____.

SCENARIO 15-7-B You are the CEO of a dairy company. You are planning to expand milk production by purchasing additional cows, lands and hiring more workers. From the existing 50 farms owned by the company, you have collected data on total milk production (in liters), the number of milking cows, land size (in acres) and the number of laborers. The data are shown below and also available in the Excel file Scenario15-7-DataB.XLSX. You believe that the number of milking cows $\left( X _ { 1 } \right)$ , land size $\left( X _ { 2 } \right)$ and the number of laborers $\left( X _ { 3 } \right)$ are the best predictors for total milk production on any given farm. -Referring to Scenario 15-7-B, there is insufficient evidence to conclude that the quadratic term for the number of milking cows is statistically significant at the 10% level of significance after you have performed a multiple regression that includes the quadratic terms for the number of milking cows, land size and the number of laborers.

SCENARIO 15-4 The superintendent of a school district wanted to predict the percentage of students passing a sixth- grade proficiency test. She obtained the data on percentage of students passing the proficiency test (% Passing), daily mean of the percentage of students attending class (% Attendance), mean teacher salary in dollars (Salaries), and instructional spending per pupil in dollars (Spending) of 47 schools in the state. -Referring to Scenario 15-4, the "best" model chosen using the adjusted R-square statistic is a) $X _ { 1 } , X _ { 3 }$ b) $X _ { 1 } , X _ { 2 } , X _ { 3 }$ c) either of the above d) None of the above

SCENARIO 15-7-A You are the CEO of a dairy company. You are planning to expand milk production by purchasing additional cows, lands and hiring more workers. From the existing 50 farms owned by the company, you have collected data on total milk production (in liters), the number of milking cows, land size (in acres) and the number of laborers. The data are shown below and also available in the Excel file Scenario15-7-DataA.XLSX. You believe that the number of milking cows $\left( X _ { 1 } \right)$ , land size $\left( X _ { 2 } \right)$ and the number of laborers $\left( X _ { 3 } \right)$ are the best predictors for total milk production on any given farm. -Referring to Scenario 15-7-A, the model that includes only $X _ { 2 } \text { and } X _ { 3 }$ should be among the appropriate models using the Mallow's Cp statistic.

SCENARIO 15-7-B You are the CEO of a dairy company. You are planning to expand milk production by purchasing additional cows, lands and hiring more workers. From the existing 50 farms owned by the company, you have collected data on total milk production (in liters), the number of milking cows, land size (in acres) and the number of laborers. The data are shown below and also available in the Excel file Scenario15-7-DataB.XLSX. You believe that the number of milking cows $\left( X _ { 1 } \right)$ , land size $\left( X _ { 2 } \right)$ and the number of laborers $\left( X _ { 3 } \right)$ are the best predictors for total milk production on any given farm. -Referring to Scenario 15-7-B, there is insufficient evidence to conclude that the quadratic term for land size is statistically significant at the 10% level of significance after you have performed a multiple regression that includes the quadratic terms for the number of milking cows, land size and the number of laborers.

SCENARIO 15-7-A You are the CEO of a dairy company. You are planning to expand milk production by purchasing additional cows, lands and hiring more workers. From the existing 50 farms owned by the company, you have collected data on total milk production (in liters), the number of milking cows, land size (in acres) and the number of laborers. The data are shown below and also available in the Excel file Scenario15-7-DataA.XLSX. You believe that the number of milking cows $\left( X _ { 1 } \right)$ , land size $\left( X _ { 2 } \right)$ and the number of laborers $\left( X _ { 3 } \right)$ are the best predictors for total milk production on any given farm. -Referring to Scenario 15-7-A, the variable $X _ { 1 }$ should be dropped to remove collinearity?

SCENARIO 15-4 The superintendent of a school district wanted to predict the percentage of students passing a sixth- grade proficiency test. She obtained the data on percentage of students passing the proficiency test (% Passing), daily mean of the percentage of students attending class (% Attendance), mean teacher salary in dollars (Salaries), and instructional spending per pupil in dollars (Spending) of 47 schools in the state. -Referring to Scenario 15-4, the residual plot suggests that a nonlinear model on % attendance may be a better model.

SCENARIO 15-7-A You are the CEO of a dairy company. You are planning to expand milk production by purchasing additional cows, lands and hiring more workers. From the existing 50 farms owned by the company, you have collected data on total milk production (in liters), the number of milking cows, land size (in acres) and the number of laborers. The data are shown below and also available in the Excel file Scenario15-7-DataA.XLSX. You believe that the number of milking cows $\left( X _ { 1 } \right)$ , land size $\left( X _ { 2 } \right)$ and the number of laborers $\left( X _ { 3 } \right)$ are the best predictors for total milk production on any given farm. -Referring to Scenario 15-7-A, there is sufficient evidence to conclude that the quadratic term for the number of laborers is statistically significant at the 10% level of significance after you have performed a multiple regression that includes the quadratic terms for the number of milking cows, land size and the number of laborers.

SCENARIO 15-7-A You are the CEO of a dairy company. You are planning to expand milk production by purchasing additional cows, lands and hiring more workers. From the existing 50 farms owned by the company, you have collected data on total milk production (in liters), the number of milking cows, land size (in acres) and the number of laborers. The data are shown below and also available in the Excel file Scenario15-7-DataA.XLSX. You believe that the number of milking cows $\left( X _ { 1 } \right)$ , land size $\left( X _ { 2 } \right)$ and the number of laborers $\left( X _ { 3 } \right)$ are the best predictors for total milk production on any given farm. -Referring to Scenario 15-7-A, the variable $X _ { 2 }$ should be dropped to remove collinearity?

SCENARIO 15-7-B You are the CEO of a dairy company. You are planning to expand milk production by purchasing additional cows, lands and hiring more workers. From the existing 50 farms owned by the company, you have collected data on total milk production (in liters), the number of milking cows, land size (in acres) and the number of laborers. The data are shown below and also available in the Excel file Scenario15-7-DataB.XLSX. You believe that the number of milking cows $\left( X _ { 1 } \right)$ , land size $\left( X _ { 2 } \right)$ and the number of laborers $\left( X _ { 3 } \right)$ are the best predictors for total milk production on any given farm. -Referring to Scenario 15-7-B, the p value of the t test statistic for testing whether the quadratic term for the number of laborers is statistically significant after you have performed a multiple regression that includes the quadratic terms for the number of milking cows, land size and the number of laborers is ______.

SCENARIO 15-6 Given below are results from the regression analysis on 40 observations where the dependent variable is the number of weeks a worker is unemployed due to a layoff $( Y )$ and the independent variables are the age of the worker $\left( X _ { 1 } \right)$ , the number of years of education received $\left( X _ { 2 } \right)$ , the number of years at the previous job $\left( X _ { 3 } \right)$ , a dummy variable for marital status ( $X _ { 4 } : 1 =$ married, $0 =$ otherwise), a dummy variable for head of household $\left( X _ { 5 } : 1 = \right.$ yes, $0 =$ no) and a dummy variable for management position $\left( X _ { 6 } : 1 = \right.$ yes, $0 =$ no $)$ . The coefficient of multiple determination $\left( R _ { j } ^ { 2 } \right)$ for the regression model using each of the 6 variables $X _ { j }$ as the dependent variable and all other $X$ variables as independent variables are, respectively, $0.2628,0.1240,0.2404,0.3510,0.3342$ and $0.0993$ . The partial results from best-subset regression are given below: Model R Square Adj. R Square Std. Error X1X5X6 0.4568 0.4116 18.3534 X1X2X5X6 0.4697 0.4091 18.3919 X1X3X5X6 0.4691 0.4084 18.4023 X1X2X3X5X6 0.4877 0.4123 18.3416 X1X2X3X4X5X6 0.4949 0.4030 18.4861 -Referring to Scenario 15-6, the model that includes $X _ { 1 } , X _ { 2 } , X _ { 3 } , X _ { 5 } \text { and } X _ { 6 }$ should be among the appropriate models using the Mallow's $C _ { p }$ statistic.

SCENARIO 15-7-A You are the CEO of a dairy company. You are planning to expand milk production by purchasing additional cows, lands and hiring more workers. From the existing 50 farms owned by the company, you have collected data on total milk production (in liters), the number of milking cows, land size (in acres) and the number of laborers. The data are shown below and also available in the Excel file Scenario15-7-DataA.XLSX. You believe that the number of milking cows $\left( X _ { 1 } \right)$ , land size $\left( X _ { 2 } \right)$ and the number of laborers $\left( X _ { 3 } \right)$ are the best predictors for total milk production on any given farm. -Referring to Scenario 15-7-A, the p value of the t test statistic for testing whether the quadratic term for the number of milking cows is statistically significant after you have performed a multiple regression that includes the quadratic terms for the number of milking cows, land size and the number of laborers is _____.

SCENARIO 15-7-B You are the CEO of a dairy company. You are planning to expand milk production by purchasing additional cows, lands and hiring more workers. From the existing 50 farms owned by the company, you have collected data on total milk production (in liters), the number of milking cows, land size (in acres) and the number of laborers. The data are shown below and also available in the Excel file Scenario15-7-DataB.XLSX. You believe that the number of milking cows $\left( X _ { 1 } \right)$ , land size $\left( X _ { 2 } \right)$ and the number of laborers $\left( X _ { 3 } \right)$ are the best predictors for total milk production on any given farm. -Referring to Scenario 15-7-B, you should not keep the quadratic term for the number of milking cows at the 10% level of significance after you have performed a multiple regression that includes the quadratic terms for the number of milking cows, land size and the number of laborers.

SCENARIO 15-7-B You are the CEO of a dairy company. You are planning to expand milk production by purchasing additional cows, lands and hiring more workers. From the existing 50 farms owned by the company, you have collected data on total milk production (in liters), the number of milking cows, land size (in acres) and the number of laborers. The data are shown below and also available in the Excel file Scenario15-7-DataB.XLSX. You believe that the number of milking cows $\left( X _ { 1 } \right)$ , land size $\left( X _ { 2 } \right)$ and the number of laborers $\left( X _ { 3 } \right)$ are the best predictors for total milk production on any given farm. -Referring to Scenario 15-7-B, you should not keep the quadratic term for land size at the 10% level of significance after you have performed a multiple regression that includes the quadratic terms for the number of milking cows, land size and the number of laborers.

A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is Measured in hundreds of square feet, income is measured in thousands of dollars, and education is In years. The builder randomly selected 50 families and constructed the multiple regression Model. The business literature involving human capital shows that education influences an Individual's annual income. Combined, these may influence family size. With this in mind, what Should the real estate builder be particularly concerned with when analyzing the multiple Regression model?

SCENARIO 15-7-A You are the CEO of a dairy company. You are planning to expand milk production by purchasing additional cows, lands and hiring more workers. From the existing 50 farms owned by the company, you have collected data on total milk production (in liters), the number of milking cows, land size (in acres) and the number of laborers. The data are shown below and also available in the Excel file Scenario15-7-DataA.XLSX. You believe that the number of milking cows $\left( X _ { 1 } \right)$ , land size $\left( X _ { 2 } \right)$ and the number of laborers $\left( X _ { 3 } \right)$ are the best predictors for total milk production on any given farm. -Referring to Scenario 15-7-A, the value of the variance inflationary factor of the number of laborers is _____.

SCENARIO 15-7-A You are the CEO of a dairy company. You are planning to expand milk production by purchasing additional cows, lands and hiring more workers. From the existing 50 farms owned by the company, you have collected data on total milk production (in liters), the number of milking cows, land size (in acres) and the number of laborers. The data are shown below and also available in the Excel file Scenario15-7-DataA.XLSX. You believe that the number of milking cows $\left( X _ { 1 } \right)$ , land size $\left( X _ { 2 } \right)$ and the number of laborers $\left( X _ { 3 } \right)$ are the best predictors for total milk production on any given farm. -Referring to Scenario 15-7-A, the value of the variance inflationary factor of the number of milking cows is _____.