Consider a regression study involving a dependent varlable y, a quantitativeindependent variable x1, and a categorical independent variable with threepossible levels (level 1, level 2, and level 3).OHOW many dummy variables are required to represent the categorical variable?10 Write a multiple regression equation relating x1, and the categorical variableto yDo NOT use EXCELOa 0 2there can be two multiple regression equations using each level1) there can be three multiple regression equations using each level(i) there can be three multiple regression equations using each levelOd 0 1) there can be two multiple regression equations using each level

Answered: Image /qna-images/answer/b87ca2eb-c7b2-4b5a-8fca-e42786fdc4e0.jpg

Answered: Consider a regression study involving a…

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter1: Functions

Section1.2: The Least Square Line

Problem 8E

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If your graphing calculator is capable of computing a least-squares sinusoidal regression model, use it to find a second model for the data. Graph this new equation along with your first model. How do they compare?
Which statement is not correct for multiple regression model? When we interpret this categorical variable, we would say the change we observe when one switches from the reference category to the specific category. The reference category will not be displayed in our model results. If we include a categorical variable with more than two values (e.g., religion) as an independent variable, we want to include a dummy variable for all categories except for two. We can include more than two categorical variables in the model. The value of the independent variable not included in the model is called "reference category."
when a regression is used as a method of predicting dependent variables from one or more independent variables. How are the independent variables different from each other yet related to the dependent variable?
XYZ company is interested in quantifying the impact of consumer promotions on the sales of its packaged food product. XYZ has historical data on the following variables for 38 weeks:• Sales: Weekly sales volume in thousands of units.• Prom: Weekly spending on consumer promotions in thousands of Dollars""A regression analysis was applied to XYZ historical dataset. The dependent variable is weekly Sales and the independent variables are weekly Prom and weekly Lagged Prom (i.e., last week Prom). This is a summary of the regression output:Sales = 0.80 + 1.20*Prom - 0.40*Lag(Prom)• R-squared=0.85• F-Statistic=23.83• p-value=0.001 (for the overall regression)•All regression coefficients are statistically significant at the 5% level."A. What is the percent of variance in sales that is explained by Prom and Lag(Prom)? B. Is the overall regression equation statistically significant at the 5% level? Give reasons for the same? C. What is the net volume impact of an incremental $1000 spending per…
XYZ company is interested in quantifying the impact of consumer promotions on the sales of its packaged food product. XYZ has historical data on the following variables for 38 weeks: • Sales: Weekly sales volume in thousands of units.• Prom: Weekly spending on consumer promotions in thousands of Dollars" "A regression analysis was applied to XYZ historical dataset. The dependent variable is weekly Sales and the independent variables are weekly Prom and weekly Lagged Prom (i.e., last week Prom). This is a summary of the regression output:Sales = 0.80 + 1.20*Prom - 0.40*Lag(Prom) • R-squared=0.85• F-Statistic=23.83• p-value=0.001 (for the overall regression)•All regression coefficients are statistically significant at the 5% level." A. What is the percent of variance in sales that is explained by Prom and Lag(Prom)?B. Is the overall regression equation statistically significant at the 5% level? Give reasons for the same? C. What is the net volume impact of an incremental $1000 spending…
10) The following results are from a regression where the dependent variable is COST OF COLLEGE and the independent variables are TYPE OF SCHOOL which is a dummy variable = 0 for public schools and = 1 for private schools, FIRST QUARTILE SAT which is the average score of students in the top quartile of SAT’s, THIRD QUARTILE SAT which is the average score of students in the 3rd quartile, and ROOM AND BOARD which is the cost of room and board at the school. The first set of results includes all the independent variables whereas the second set of results excludes the THIRD QUARTILE SAT variable. a) Based on these two sets of data, does there appear that multicollinearity is a problem (specifically, does it appear that THIRD QUARTILE SAT is highly collinear with the other independent variables? Explain. b) Calculate the VIF for THIRD QUARTILE SAT. c) Based on the VIF, do you think that multicollinearity is a problem? Explain.
Show that an interaction term of a dummy variable and a regressor changes the slope of a regression line..
Identify two different conditions under which the regression line should not be used to make predictions.
A researcher is interested to find out how the engine displacement, vehicle weight, and the type of transmission [i.e. automatic & manual] affect the automobile gasoline mileage. Type of transmission is represented by one dummy variable: automatic (=1, if transmission is automatic; = 0, if transmission is manual) Part of the raw data and the regression output of 40 different car models are given below. Automobile Miles/gallon Displacement(cubic in) Weight(lb)) Automatic Trans. Corvette 22.50 x x x Cruiser 19.30 x x x Omega x 440 x x Nova x 514 x x Corolla E5 x x 5911 x Cougar x x 3800 x Starfire x x x 0 Cordoba x x x 1 SUMMARY OUTPUT Regression Statistics Multiple R 0.874319 R Square xxx Adjusted R Square xxx Standard Error 3.395 Observations 40…
A researcher is interested to find out how the engine displacement, vehicle weight, and the type of transmission [i.e. automatic & manual] affect the automobile gasoline mileage. Type of transmission is represented by one dummy variable: automatic (=1, if transmission is automatic; = 0, if transmission is manual) Part of the raw data and the regression output of 40 different car models are given below. Automobile Miles/gallon Displacement(cubic in) Weight(lb)) Automatic Trans. Corvette 22.50 x x x Cruiser 19.30 x x x Omega x 440 x x Nova x 514 x x Corolla E5 x x 5911 x Cougar x x 3800 x Starfire x x x 0 Cordoba x x x 1 SUMMARY OUTPUT Regression Statistics Multiple R 0.874319 R Square xxx Adjusted R Square xxx Standard Error 3.395 Observations 40…
A business statistics professor would like to develop a regression model to predict the final exam scores for students based on their current GPAs, the number of hours they studied for the exam, the number of times they were absent during the semester, and their genders. The data for these variables are given in the accompanying table at the bottom of this page. a) Using Excel, construct a regression model using all of the independent variables. Create the dummy variable Gen, which equals 1 for a male and 0 for a female student ( this assignment is arbitrary) complete the regression equation for the model below, where y= Score, x1= GPA, x2= Hours, x3= Absenses, and x4= Gen. y= (__) + (__)x1 + (__)x2 + (__)x3 + (__)x4 b) Test the significance of the overall regression model using a= 0.10. c) interpret the meaning of the regression coefficient for the dummy variable. d) using the p-values, identify which independent variables are significant with a= 0.10. e) construct a regression…

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