What is the significance of R and R2 and of a regression model?

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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What is the difference between the following two regression equations? y=b0+b1x y=B0+B1x
A county real estate appraiser wants to develop a statistical model to predict the appraised value of houses in a section of the county called East Meadow. One of the many variables thought to be an important predictor of appraised value is the number of rooms in the house. Consequently, the appraiser decided to fit the simple linear regression model, y = b₁x + bowhere y = appraised value of the house (in $thousands) and x = number of rooms. Using data collected for a sample of n=74 houses in East Meadow, the following results were obtained: y=74.80+ 17.80x Give a practical interpretation of the estimate of the slope of the least squares line. For each additional room in the house, we estimate the appraised value to increase $74,800. 1000 For each additional dollar of appraised value, we estimate the number of rooms in the house to increase by 17.80 rooms. For a house with 0 rooms, we estimate the appraised value to be $74,800. For each additional room in the house, we estimate the…
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."
A researcher predicts that gender (male and female) and race (race 1, race 2 and race 3) are factors which determine the willingness of a person to get involved in politics. He plan to use a multiple regression test to analyse his data. Is the multiple regression test appropriate for the study? Elaborate on your answer.
To properly examine the effect of a categorical independent variable in a multiple linear regression model we use an interaction term. True O False
Briefly describe what is meant by the problem of errors in measurement of the predictor variables and describe its effect on a regression analysis.
3) What is the use of regression analysis (Please support your answer with a suitable example)? Driving Experience (years) Monthly Auto Insurance Premium 5 $64 2 87 12 50 9 71 15 44 6 56 25 42 16 60 Does the insurance premium depend on the driving experience or does the driving experience depend on the insurance premium? Do you expect a positive or a negative relationship between these two variables?
When you are deciding which variables to include as predictors in a multiple regression equation, what are some conditions that you must consider first?
In order to explain the U.S. defense budget, the following variables are considered. Data from 1962-1981 is collected. Variable Definition Y Defense budget-outlay for year t, $ billions X2 GNP for year t, $ billions X3 U.S. military sales/assistance in year t, $ billions X4 Aerospace industry sales, $ billions Dependent Variable: Y Method: Least Squares Date: 11/22/21 Time: 11:20 Sample: 1962 1981 Included observations: 20 Variable Coefficient Std. Error t-Statistic Prob. X2 0.016703 0.007017 2.380261 0.0301 X3 -0.696174 0.453978 -1.533497 0.1447 X4 1.467729 0.277608 5.287047 0.0001 22.77514 3.311695 6.877186 0.0000 R-squared 0.971088 Mean dependent var 83.86000 Adjusted R-squared 0.965667 S.D. dependent var 28.97771 S.E. of regression Sum squared resid 5.369339 Akaike info criterion 6.376143 461.2769 Schwarz criterion 6.575290 Log likelihood -59.76143 Hannan-Quinn criter. 6.415019 F-statistic 179.1337 Durbin-Watson stat 0.676777 Prob(F-statistic) 0.000000
When comparing different multiple linear regression models to determine which is better for predicting a response variable, Y, why should we use the adjusted-R2 values instead of the plain R2 values?
How would a researcher know whether linear regression was the appropriate statistical technique to use? What are some of the benefits of fitting the relationship between two variables to an equation for a straight line? (Don't hand writing solution)
A video game designer was attempting to balance their online multiplayer mode since people were complaining that it wasn’t competitive. In order to make it more fair they decided that the amount of experience received should be balanced based on how big the level difference is between the player and the player’s opponent. To that end they devised the following regression model: Experience Gain = -14 + 21.05 Level Difference. They also calculated the coefficient of determination to be 0.96. If the level difference is 4 how much experience should the player receive? If a user gained 65 points of experience, what was the level difference? What are the y-intercept and slope of this regression model and what do they tell us? Is this a fair way to balance the game? Why or Why not?

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