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Discuss the FIVE (5) importance of adding error term in the regression model.
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- What is difference between regression model, and estimated regression equation?(2)What would the consequence be for a regression model if theerrors were not homoscedastic?1. An analyst ran a regression with four predictor variables. Variable description Variable Name Salary in R1000.00 Years at company Age in years Education in years SALARY YEARS AGE EDYEARS He suspects that AGE can be dropped from the model and he decided to employ forward stepwise regression. Show all the steps he has to do to get to a fitted response regression without age. 2. BIC, Bayesian information criteria or SBC, Schwarz' Bayesian Criteria, are the same. Give the aquations for AIC and BIC and explain the difference in these two equations in terms of the terms in the equations as well as the consequences. 3. Give a short description of measuring the actual predictive capabilities of the selected regression. model.
- As an auto insurance risk analyst, it is your job to research risk profiles for various types of drivers. One common area of concern for auto insurance companies is the risk involved when offering policies to younger, less experienced drivers. The U.S. Department of Transportation recently conducted a study in which it analyzed the relationship between 1) the number of fatal accidents per 1000 licenses, and 2) the percentage of licensed drivers under the age of 21 in a sample of 42 cities. Your first step in the analysis is to construct a scatterplot of the data. FIGURE. SCATTERPLOT FOR U.S. DEPARTMENT OF TRANSPORATION PROBLEM U.S. Department of Transportation The Relationship Between Fatal Accident Frequency and Driver Age 4.5 3.5 3 2.5 1.5 1 0.5 6. 10 12 14 16 18 Percentage of drivers under age 21 Upon visual inspection, you determine that the variables do have a linear relationship. After a linear pattern has been established visually, you now proceed with performing linear…What is a linear regression model? What is measured by the coefficients ofa linear regression model? What is the ordinary least squares estimator?Analysis of Variance Source DF SS MS Regression 1 02364 13 14 Residual Error Total 11.3240 What is the value of SSR (Sums of Squares for Regression)?
- Water is being poured into a large, cone-shaped cistern. The volume of water, measured in cm³, is reported at different time intervals, measured in seconds. A regression analysis was completed and is displayed in the computer output. Regression Analysis: cuberoot (Volume) versus Time Predictor Coef SE Coef Constant -0.006 0.00017 -35.294 0.000 Time 0.640 0.000018 35512.6 0.000 s=0.030 R-Sq=1.000 R-sq (adj)=1.000 What is the equation of the least-squares regression line? Volume = 0.640 - 0.006(Time) Volume = 0.640 - 0.006(Time) Volume = -0.006 + 0.640(Time) Volume = - 0.006 + 0.640(Time?)Consider the following computer output of a multiple regression analysis relating annual salary to years of education and years of work experience. Regression Statistics Multiple R 0.7339 R Square 0.5386 Adjusted R Square 0.5185 Standard Error 2137.5200 Observations 49 ANOVA SS df Regression 2 245,370,679.3850 122,685,339.6925 26.8517 MS F Significance F 1.9E-08 Residual 46 210,173,612.6150 Total 48 455,544,292.0000 4,568,991.5786 Coefficients Standard Error Intercept Education (Years) 14290.37278 2350.8671 2,528.5819 338.1140 Experience (Years) 829.3167 392.5627 t Stat P-value 5.6515 0.000000961 6.9529 0.000000011 2.1126 0.040093183 Lower 95 % Upper 95 % 9200.6014 19,380.1442 1670.2789 3031.4553 39.129 1619.5044 Step 1 of 2: What would be your expected salary with no education and no experience?Explain what is meant by an error term. What assumptions do we makeabout an error term when estimating an ordinary least squares regression?
- Consider the following computer output of a multiple regression analysis relating annual salary to years of education and years of work experience. Regression Statistics Multiple R 0.7339 R Square 0.5386 Adjusted R Square 0.5185 Standard Error 2137.5200 Observations 49 ANOVA SS df Regression 2 245,370,679.3850 122,685,339.6925 26.8517 MS F Significance F 1.9E-08 Total Residual 46 210,173,612.6150 48 455,544,292.0000 4,568,991.5786 Coefficients Standard Error Intercept Education (Years) 14290.37278 2350.8671 2,528.5819 338.1140 Experience (Years) 829.3167 392.5627 t Stat P-value 5.6515 0.000000961 9200.6014 6.9529 0.000000011 2.1126 0.040093183 Lower 95 % Upper 95% 19,380.1442 1670.2789 3031.4553 39.129 1619.5044 Step 2 of 2: How much would you expect your salary to increase if you had one more year of education?Table 4.1 SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square 0.99794806 Missing 0.99513164 Standard Error 1.64839211 Observations 20 ANOVA Significance F af Missing 16 19 MS F Regression 10561.07486 Missing 1295.585 2.66E-19 Residual 43.47514498 2.717197 Total 10604.55 Coefficients 0.562 Standard Error t Stat P-Value Intercept X1 1.327 0.424 0.677 0.959 0.038 25.245 0.000 X2 1.117 0.125 8.916 0.000 X3 1.460 0.066 22.185 0.000 Consider the output shown in Table 4.1. Which of the predictors has the greatest impact on the dependent variable? X2 Intercept X1 X31. You are interested the causal effect of X on Y, B1. Suppose that X, and X2 are uncorrelated. You estimate B1 by regressing Y onto X1 (so that X2 is not included in the regression). Does this estimator suffer from omitted variable bias due to the exclusion of X2? (a) Yes (b) No (c) Maybe 2. Omitted variable bias violates which of the following assumptions: (a) The conditional distribution of u, given X1i X2i, ...Xki has a mean of zero (b) (Xi, X2i...Y;), i = 1, ., n are independently and identically distributed (c) Heteroskedasticity (d) Perfect multicollinearity