Exam 15: Multiple Regression

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 quadratic effect of daily average of the percentage of students attending class on percentage of students passing the proficiency test is not significant at a 5% level of significance.

If a group of independent variables are not significant individually but are significant as a group at a specified level of significance, this is most likely due to

SCENARIO 15-5 What are the factors that determine the acceleration time (in sec.) from 0 to 60 miles per hour of a car? Data on the following variables for 171 different vehicle models were collected: Accel Time: Acceleration time in sec. Cargo Vol: Cargo volume in cu. ft. HP: Horsepower MPG: Miles per gallon SUV: 1 if the vehicle model is an SUV with Coupe as the base when SUV and Sedan are both 0 Sedan: 1 if the vehicle model is a sedan with Coupe as the base when SUV and Sedan are both 0 The coefficient of multiple determination $\left( R _ { j } ^ { 2 } \right)$ for the regression model using each of the 5 variables $X _ { j }$ as the dependent variable and all other $X$ variables as independent variables are, respectively, $0.7461,0.5676,0.6764,0.8582,0.6632$ . -Referring to Scenario 15-5, what is the value of the variance inflationary factor of Sedan?

SCENARIO 15-1 A certain type of rare gem serves as a status symbol for many of its owners. In theory, for low prices, the demand increases and it decreases as the price of the gem increases. However, experts hypothesize that when the gem is valued at very high prices, the demand increases with price due to the status owners believe they gain in obtaining the gem. Thus, the model proposed to best explain the demand for the gem by its price is the quadratic model: $Y = \beta _ { 0 } + \beta _ { 1 } X + \beta _ { 2 } X ^ { 2 } + \varepsilon$ where Y = demand (in thousands) and X = retail price per carat. This model was fit to data collected for a sample of 12 rare gems of this type. A portion of the computer analysis obtained from Microsoft Excel is shown below: -Referring to Scenario 15-1, what is the correct interpretation of the coefficient of multiple determination?

Using the $C _ { p } \text { statistic in model building, all models with } C _ { p } \leq ( k + 1 ) \text { are equally }$ good.

Which of the following will NOT change a nonlinear model into a linear model?