7. In multiple regression model $y_i = \beta_0 + \beta_1 x_{i1} + \beta_2 x_{i2} + u_i$. The sales data is regressed on AdCost and Enemp variables. Answer following questions and report your findings (Data is given in table 1). a. Fit the multiple linear regression model in incremental order. And report your findings? Also Interpret ate each individual parameter and also discuss which one is more important. (10) b. How do you perform a test of the overall significance of the regression model? What are the null and alternative hypotheses for this test? What is the rejection rule? What is the intuition for why the test works? Explain. (7.5) c. How do you perform a test of the individual significance of a slope coefficient of the regression function? What are the null and alternative hypotheses for this test? What is the rejection rule? What is the intuition for why the test works? Explain. (7.5) Table1 Month Sales AdCost Unemp 1 27 550 4.6 2 24.2 425 4.3 3 25.6 450 4.6 4 28.5 625 4.3 5 30.8 650 4.8 6 31.5 675 5.2 7 34.9 700 5.6 8 32.5 650 5.8 9 30.4 550 5.5 10 31 525 5.8 11 28.5 500 6 12 29 600 6.5 13 26.2 575 8 14 25.4 625 8.4 15 27.8 650 9.1 16 26.5 600 8.9 17 27.4 550 9.1
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To fit the multiple linear regression model, we will use the given data in Table 1 with Sales as the dependent variable and AdCost and Unemp as independent variables. The regression model can be written as: hat(y)_(i) = hat(\beta )_(0) + hat(\beta )_(1)x_(1i) + Show more…
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2. How are the sales and the shelf space correlated with each other? Explain your answer. 3. How much variation in the sales is explained by the shelf space based on the sample? Explain your answer. 4. How much is the sum of squares residual? 5. Write the hypothesis statements to test the regression model's overall significance. 6. Calculate the F statistic for the test of the overall significance of the regression model. 7. What conclusion can be drawn on the overall significance of the regression model? Explain your answer. 8. Write the estimated regression equation. 9. Calculate the t statistic for the coefficient on the shelf space 10. What conclusion can be drawn on the significance of the coefficient on the shelf space? 11. Explain the coefficient on the shelf space. 12. According to the estimated model, how much are sales predicted to be given that shelf space is 4.5 feet?
Dominador T.
(a) Use a calculator’s regression (REG) function to compute the sample estimates, b0 and b1 of the population regression coefficients, determine the estimated regression equation and find out the linear correlation coefficient (r) and Sxx. [5] (b) Interpret the meaning of the value of the linear correlation coefficient (r). [2] (c) Perform a regression t-test. Does the t-test indicate a significant relationship between the number of cans bought and the number of advertisements read or seen at the 5% level? The test must include the following parts: (i) State the hypotheses to be tested. [2] (ii) Determine the rejection region. [2] (iii) Given that se = 2.1064 , compute the value of the test statistic. [3] (iv) State the decision to be made and draw your conclusion. [3] (d) Find the 95% confidence interval for β1. [3] (e) Construct a 95% prediction interval estimate of the number of cans purchased for an individual with the number of advertisements seen 6 times in the past week. [5]
Sheryl E.
The following questions are related to a generalized linear regression model. What are the 3 components of a generalized linear model? For a logistic regression of lung cancer incidences (1=developed lung cancer, 0=did not develop lung cancer) with smoking statuses (1=current or past smoker, 0=never smoker), specify the 3 components that you identified in part a. A study was conducted to investigate the effects of AZT treatment on the development of AIDS symptoms among HIV-infected veterans. Among 170 individuals who took AZT, 25 developed the symptoms of AIDS by the end of the study. Among the other 168 individuals who did not take AZT (placebo group), 44 developed the symptoms of AIDS. Construct a two-by-two table. Use AIDS symptoms as columns and AZT treatment as rows. Based on the table constructed in a., calculate the odds of AIDS in the treatment group, odds of AIDS in the placebo group, and the odds ratio of AIDS comparing the treatment and placebo group. If we fit a logistic regression model of the development of AIDS symptoms on AZT based on the data provided, write down the model (No need to specify three components in GLM, write one formula connecting the probability of developing AIDS and AZT. Hint: you need to create a dummy variable for AZT). Without fitting the regression model in c. via Stata, give estimates of the coefficient betas. Suppose race (1=white, 0=nonwhite) is a potential confounder and we fit a logistic regression model for the development of AIDS symptoms on AZT (1=users, 0=nonuser), race (1=white, 0=nonwhite), and the interaction between AZT and race. Using the output shown below, estimate the probability of developing AIDS symptoms during the study follow-up for a nonwhite AZT user. [Stata] Property Valuation: Scientific mass appraisal uses linear regression methods to assess property valuation. Twenty-four observations were obtained from a property listing for Champaign IL. The problem is to find the best fitting regression model to predict the sales price (y) using the following independent variables: taxes in $1000s of dollars (x1), number of bedrooms (x2), age of the home in years (x3). The data set is stored in the midterm.dta file. Answer the following questions, justifying with appropriate analyses. Do not just answer yes or no, you must justify your response and provide data to back it up. In a fitted regression model that relates the sale price to taxes and building characteristics, would you include all the variables? (Hint: Are all the variables significant?) A veteran real estate agent has suggested that a model with taxes and the number of bedrooms should adequately describe the sales price. Do you agree? Present what you consider to be the most adequate model or models for predicting the sale price of homes in Champaign IL. ID x1 x2 x3 y 1 4.918 4 42 25.9 2 5.021 4 62 29.5 3 4.543 3 40 27.9 4 4.557 3 54 25.9 5 5.06 3 42 29.9 6 3.891 3 56 29.9 7 5.898 3 51 30.9 8 5.604 3 32 28.9 9 5.828 3 32 35.9 10 5.3 3 30 31.5 11 6.271 2 30 31 12 5.959 3 32 30.9 13 5.05 2 46 30 14 8.246 4 50 36.9 15 6.697 3 22 41.9 16 7.784 3 17 40.5 17 9.038 3 23 43.9 18 5.989 3 40 37.9 19 7.542 3 22 37.9 20 8.795 4 50 44.5 21 6.083 3 44 37.9 22 8.361 4 48 38.9 23 8.14 3 3 36.9 24 9.142 4 31 45.8
Patha S.
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