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

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Answered: Consider a regression study involving a…

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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Consider a regression study involving a dependent variable y, a quantitative independent variable x1, and a categorical independent variable with three possible levels (level 1, level 2, and level 3). (i) How many dummy variables are required to represent the categorical variable? (ii) Write a multiple regression equation relating x1, and the categorical variable to y. PLEASE SHOW ALL HAND WRITTEN STEPS AND DO NOT USE EXCEL OR ANY SOFTWARE
In reading the results of a multiple regression analysis that contained 4 predictor variables, the researcher noticed a column labeled Beta. Two of the Beta’s were positive and two were negative. He concluded that a.) Beta’s that were positive were statistically significant b.) Beta’s that were positive had more of an effect c.) Beta’s that were positive were associated with increases in the criterion variable d.) Beta’s that were positive did not affect the criterion because they were “controlled for…”
The least-squares regression line relating two statistical variables is given as = 24 + 5x. Compute the residual if the actual (observed) value for y is 38 when x is 2. 4 38 2
Data was collected on 54 observations on a response of interest, y, and four potential predictor variables x1, x2, x3, and x4. The output from regression analyses of the data is attached to the end of the page. d) Is the variable from your best simple linear regression model (from part a) included in the model with the lowest overall MSE (part b)? Briefly explain why it could happen that the best single variable is not in the best overall model. e) Following the best subsets regression results, the sums of squares for regression and error (also called residual) are displayed for several models. Using the regression sums of squares information for the full model containing all four x variables, calculate i) the R2 value for the full model, ii) the F statistic for the test of the H0: b1 = b2 = b3 = b4 = 0, and iii) the standard deviation of the residuals for the full model. f) Using the regression sums of squares information, test the null hypothesis H0:b2 = b4 = 0 for the full model.…
The Wall Street Journal asked Concur Technologies, Inc., an expense management company, to examine data from 8.3 million expense reports to provide insights regarding business travel expenses. Their analysis of the data showed that New York was the most expensive city. The following table shows the average daily hotel room rate (X) and the average amount spent on entertainment (Y) for a random sample of 9 of the 25 most-visited U.S. cities. These data lead to the estimated regression equation y = 17.49 + 1.0334x. For these data SSE = 1541.4. Use Table 1 of Appendix B. a. Predict the amount spent on entertainment for a particular city that has a daily room rate of $89 (to 2 decimals). b. Develop a 95% confidence interval for the mean amount spent on entertainment for all cities that have a daily room rate of $89 (to 2 decimals). c. The average room rate in Chicago is $128. Develop a 95% prediction interval for the amount spent on entertainment in Chicago (to 2 decimals).
The Wall Street Journal asked Concur Technologies, Inc., an expense management company, to examine data from 8.3 million expense reports to provide insights regarding business travel expenses. Their analysis of the data showed that New York was the most expensive city. The following table shows the average daily hotel room rate (X) and the average amount spent on entertainment (Y) for a random sample of 9 of the 25 most-visited U.S. cities. These data lead to the estimated regression equation y = 17.49 + 1.0334x. For these data SSE = 1541.4. Use Table 1 of Appendix B. (NEED ANSWER FOR A) a. Predict the amount spent on entertainment for a particular city that has a daily room rate of $89 (to 2 decimals).
Select one: True False a.In regression analysis, the dependent variable is a variable whose value is unknown and is being explained or predicted with the help of another variable. b.In developing a simple linear regression model, only one independent variable is used to explain the variation in a single dependent variable. c.In a simple linear regression model, if you found that the true regression coefficient is significantly greater than zero, then you may also conclude that the two variables are positively correlated.
In this section, we used the statistic b1 as a basis for conducting a hypothesis test to decide whether a regression equation is useful for prediction. Identify two other statistics that can be used as a basis for such a test.
The data from exercise 3 follow. xi 2 6 9 13 20 yi 7 18 9 26 23 The estimated regression equation is = 7.6 + .9x. What is the value of the standard error of the estimate (to 4 decimals)? What is the value of the t test statistic (to 2 decimals)? What is the p-value? Use Table 1 of Appendix B.Selectless than .01between .01 and .02between .02 and .05between .05 and .10between .10 and .20between .20 and .40greater than .40Item 3 What is your conclusion ( = .05)?SelectConclude a significant relationship exists between x and yCannot conclude a significant relationship exists between x and yItem 4 Use the F test to test for a significant relationship. Use = .05.Compute the value of the F test statistic (to 2 decimals). What is the p-value?Selectless than .01between .01 and .025between .025 and .05between .05 and .10greater than .10Item 6 What is your conclusion?SelectConclude a significant relationship exists between x and yCannot conclude a significant relationship exists…
A multiple linear regression model based on a sample of 13 weeks is developed to predict standby hours based on the total staff present and remote hours. The SSR is 23,638.17 and the SSE is 33,273.99. a. Determine whether there is a significant relationship between standby hours and the two independent variables (total staff present and remote hours) at the 0.05 level of significance. What are the correct hypotheses to test?
A researcher would like to predict the dependent variable Y from the two independent variables X1 and X2 for a sample of N=10 subjects. Use multiple linear regression to calculate the coefficient of multiple determination and test statistics to assess the significance of the regression model and partial slopes. Use a significance level α=0.05. X1 X2 Y 31.9 50.2 89.2 12.7 25.5 33.5 41.2 46.4 44.5 29.2 42.9 76.3 22.9 36.6 56 39.4 46.6 55.3 36.4 46.2 43 56.1 49.6 7.6 21 39.7 58.2 58 48.3 22.6 R2=F= P-value for overall model = t1= for b1, P-value = t2= for b2, P-value = What is your conclusion for the overall regression model (also called the omnibus test)? The overall regression model is statistically significant at α=0.05. The overall regression model is not statistically significant at α=0.05. Which of the regression coefficients are statistically different from zero? neither regression coefficient is statistically significant the slope for the first…
A study is conducted to determine if there is a relationship between the two variables, blood haemoglobin (Hb) levels and packed cell volumes (PCV) in the female population. A simple linear regression analysis was performed using SPSS. Based on the SPSS output of the ANOVA table, which of the following statements is the CORRECT interpretation? 1. The regression model statistically significantly predicts the blood haemoglobin level. 2. About 39.98 % of variance in Hb is explained by PCV. 3. The regression model does not fit the data. 4. There is significant contribution of Hb towards PCV.

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