We ran a multiple regresssion model with three predictor variables with the partial Excel output shown above. To test for the usefulness of the model, the computed F-value and the P-value, respectively, are:
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- 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 2In a multiple linear regression model with 3 predictor variables, what is the t-statistic for the hypothesis test of the null hypothesis that the coefficient of the second predictor variable is equal to 0, if the estimated coefficient is 0.5, the standard error of the estimate is 0.1, and the degrees of freedom is 15?An urban community wants to show that the incidence of breast cancer is higher in their locality than in a neighboring rural area. (PCB levels were found to be higher in the soil of the urban community). If you find that in the urban community 20 out of 200 adult women have breast cancer and that in the rural community 10 out of 150 adult women have it, could you conclude, at a significance level of 0.05, that breast cancer is more prevalent in the urban community?1. The parameter of interest is:2. The hypotheses for this test are:3. The calculated test statistic is:4. The critical region is:5. Draw the critical region (make decision):6. It can be concluded that:
- A Ross MAP team is currently developing a regression model to explain the travel expense of HR consulting firms in a month (measured in thousands of dollars). So far, the team has identified the number of consultants, the number of clients, the number of air-travel trips, and the number of trips to high-expense cities (e.g., NYC, Boston, San Jose) as potential independent variables. A partial output of the corresponding regression model is in Figure 1. Use the figure to answer question 4to6 4. What is the R2 and adjusted R2 of the model? 5. What is the standard error of the estimates (serror) in thousands of dollars? 6. Based on what you can learn from this table, what is your assessment about the model? For your information, the firm with the lowest travel expense was $47K and the firm with the highest expense was $125K in the sample data.An econometrician suspects that the residuals of her model might be autocorrelated. Explain the steps involved in testing this theory using the Durbin–Watson (DW) testA researcher would like to predict the dependent variable YY from the two independent variables X1 and X2 for a sample of N=13 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=0.01. X1 X2 Y 38.3 52.7 55.5 50.9 76 89.3 33.5 57.6 18.6 40.9 43.6 27.7 48.7 63.5 76.5 49.6 73.3 57.4 36.9 53.3 29.8 35.4 62.8 50.2 39 76.3 65.4 64.9 57.7 71.5 54.8 58 51.5 37.8 62.6 54.7 56.7 50.5 36.6 R2=F= P-value for overall model = t1=for b1, P-value = t2= for b2, P-value =
- A researcher notes that, in a certain region, a disproportionate number of software millionaires were born around the year 1955. Is this a coincidence, or does birth year matter when gauging whether a software founder will besuccessful? The researcher investigated this question by analyzing the data shown in the accompanying table. Complete parts a through c below. a. Find the coefficient of determination for the simple linear regression model relating number (y) of software millionaire birthdays in a decade to total number (x) of births in the region. Interpret the result. The coefficient of determination is 1.___? (Round to three decimal places as needed.) This value indicates that 2.____ of the sample variation in the number of software millionaire birthdays is explained by the linear relationship with the total number of births in the region. (Round to one decimal place as needed.) b. Find the coefficient of determination for the simple linear regression model…Consider the multiple regression model shown next between the dependent variable Y and four independent variables X1, X2, X3, and X4, which results in the following function:Ŷ = 33 + 8X1 − 6X2 + 16X3 + 18X4For this model, there were 35 observations; SSR = 1,544 and SSE = 600. Assume a 0.01 significance level.Based on the given information, which of the following conclusions is correct about the statistical significance of the overall model? Multiple Choice Reject the null hypothesis that β3 = 0. Do not reject the null hypothesis that β1 = β2 = β3 = β4 = 0. Reject the null hypothesis that β1 = 0. Reject the null hypothesis that β1 = β2 = β3 = β4 = 0.The owner of Showtime Movie Theaters, Inc., would like to predict weekly gross revenue as a function of advertising expenditures. Historical data for a sample of eight weeks follow. Weekly Gross Revenue ($1000s) Televison Advertising ($1000s) Newspaper Advertising ($1000s) 97 6 1.5 90 2 2 95 5 1.5 93 3.5 2.5 95 3 4.3 95 3.5 3.3 95 3.5 4.2 95 4 2.5 a. Use alpha= 0.01 to test the hypotheses Ho : Beta Sub1= Beta Sub2 =0 Ha : Beta Sub1 and/or Beta Sub2 is not equal to zero for the model y=Beta Sub 0+ Beta Sub1 Xsub1+Beta Sub2 Xsub2+E , where X1= television advertising ($1000s) X2+ newspaper advertising ($1000s) Compute the F test statistic (to 2 decimals). Use F table. What is the p-value? - Select your answer -less than .01between .01 and .025between .025 and .05between .05 and .10greater than .10Item 2 What is your conclusion? - Select your answer -The overall model is not significantThe overall model is significantItem 3 b. Use alpha =0.05 to…
- Suppose the simple linear regression model, Yi = β0 + β1 xi + Ei, is used to explain the relationship between x and y. A random sample of n = 12 values for the explanatory variable (x) was selected and the corresponding values of the response variable (y) were observed. A summary of the statistics is presented in the photo attached. Let b1 denote the least squares estimator of the slope coefficient, β1. What is the value of b1?The Turbine Oil Oxidation Test (TOST) and the Rotating Bomb Oxidation Test (RBOT) are two different procedures for evaluating the oxidation stability of steam turbine oils. An article reported the accompanying observations on x = TOST time (hr) and y = RBOT time (min) for 12 oil specimens. TOST 4200 3600 3750 3650 4050 2770 RBOT 370 345 375 315 350 205 TOST 4870 4525 3450 2700 3750 3325 RBOT 400 380 285 220 345 290 (a) Calculate the value of the sample correlation coefficient. (Round your answer to four decimal places.) r = Carry out a test of hypotheses to decide whether RBOT Time and TOST time are linearly related. (Use ? = 0.05.) Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to three decimal places.) t = P-value =Suppose a researcher is interested inthe effectiveness in a new childhood exercise program implemented in a SRS of schools across a particular county. In order to test the hypothesis that the new program decreases BMI (Kg/m2), the researcher takes a SRS of children from schools where the program is employed and a SRS from schools that do not employ the program and compares the results. Assume the following table represents the SRSs of students and their BMIs. Student intervention group BMI (kg/m2) Student control group BMI (kg/m2) A 18.6 A 21.6 B 18.2 B 18.9 C 19.5 C 19.4 D 18.9 D 22.6 E 24.1 F 23.6 A) Assuming that all the necessary conditions are met (normality, independence, etc.) carry out the appropriate statistical test to determine if the new exercise program is effective. Use an alpha level of 0.05. Do not assume equal variances.B) Construct a 95% confidence interval about your estimate for the average difference in BMI between the groups.