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- 11) A simple linear regression model based on 20 observations. The F-stat for the model is 21.44 and the SSE is 1.41. The standard error for the coefficient of X is 0.2. a) Complete the ANOVA table. b) Find the t-stat of the co-efficient of X c) Find the co-efficient of X.Heights (cm) and weights (kg) are measured for 100 randomly selected adult males, and range from heights of 133 to 188 cm and weights of 40 to 150 kg. Let the predictor variable x be the first variable given. The 100 paired measurements yield x = 167.54 cm, y = 81.35 kg, r=0.186, P-value = 0.064, and y = - 109 + 1.12x. Find the best predicted value of ŷ (weight) given an adult male who is 180 cm tall. Use a 0.10 significance level. The best predicted value of y for an adult male who is 180 cm tall is (Round to two decimal places as needed.) kg.Heights (cm) and weights (kg) are measured for 100 randomly selected adult males, and range from heights of 138 to 188 cm and weights of 40 to 150 kg. Let the predictor variable x be the first variable given. The 100 paired measurements yield x = 167.61 cm, y = 81.52 kg, r=0.271, P-value=0.006, and y = -103 +1.18x. Find the best predicted value of ŷ (weight) given an adult male who is 155 cm tall. Use a 0.10 significance level. The best predicted value of y for an adult male who is 155 cm tall is (Round to two decimal places as needed.) kg.
- Suppose that I want to estimate the effect of x₁ on y. Consider the univariate regression line: how to calculate a and b₁ using OLS? y = a + b₁x₁A pharmaceutical company has developed a drug that is expected to reduce hunger. To test the drug, three samples of rats are selected with n=10n=10 in each sample. The first sample receives the drug every day. The second sample is given the drug once a week, and the third sample receives no drug at all (the control group). The dependent variables is the amount of food eaten by each rat over a 1-month period. These data are analyzed by an ANOVA, and the results are reported in the following summary table. Fill in all missing values in the table. (Hint: Start with the df column.) S.S. d.f. M.S. F Between 6.68 Within 4.35 TOTAL Use the =FDIST() function in Excel to locate the p-value for this ANOVA:p-value = Report p-value accurate to at least 6 decimal places.If you use a significance level of α=.05α=.05, what would you conclude about these treatments?Students who complete their exams early certainly can intimidate the other students, but do the early finishers perform significantly differently than the other students? A random sample of 37 students was chosen before the most recent exam in Prof. J class, and for each student, both the score on the exam and the time it took the student to complete the exam were recorded. a. Find the least-squares regression equation relating time to complete (explanatory variable, denoted by x, in minutes) and exam score (response variable, denoted by y) by considering Sx = 15, sy = 17,r = 39.706, x = 90, ỹ = 78 b. The standard error of the slope of this least-squares regression line was approximately (Sp) is 20.13. Test for a significant positive linear relationship between the two variables exam score and exam completion time for students in Prof. J's class by doing a hypothesis test regarding the population slope B1. Write the null and Alternate hypothesis and conclude the results. (Assume that…
- Heights (cm) and weights (kg) are measured for 100 randomly selected adult males, and range from heights of 132 to 193 cm and weights of 39 to 150 kg. Let the predictor variable x be the first variable given. The 100 paired measurements yield x = 167.59 cm, y = 81.52 kg, r= 0.416, P-value = 0.000, and y = - 102 + 1.13x. Find the best predicted value of y (weight) given an adult male who is 147 cm tall. Use a 0.05 significance level. The best predicted value of y for an adult male who is 147 cm tall is kg. (Round to two decimal places as needed.)Heights (cm) and weights (kg) are measured for 100 randomly selected adult males, and range from heights of 137 to 189 cm and weights of 37 to 150 kg. Let the predictor variable x be the first variable given. The 100 paired measurements yield x = 167.50 cm, y =81.41 kg, r=0.232, P-value = 0.020, and y = - 109 + 1.17x. Find the best predicted value of y (weight) given an adult male who is 145 cm tall. Use a 0.01 significance level. The best predicted value of y for an adult male who is 145 cm tall is kg. (Round to two decimal places as needed.)PLE collects a variety of data from special studies, many of which are related to the quality of its products. The company collects data about functional test performance of its mowers after assembly; results from the past 30 days are given in the worksheet Mower Test. In addition, many in-process measurements are taken to ensure that manufacturing processes remain in control and can produce according to design specifications. The worksheet Blade Weight shows 350 measurements of blade weights taken from the manufacturing process that produces mower blades during the most recent shift. Elizabeth Burke has asked you to study these data from an analytics perspective. Drawing upon your experience, you have developed a number of questions: For the mower test data, what distribution might be appropriate to model the failure of an individual mower? What fraction of mowers fails the functional performance test using all the mower test data? What is the probability of having x failures in the…
- A company studying the productivity of its employees on a new information system was interested in determingg if the age (X) of data entry opeertors influenced the number of completed entries made per hour (Y). The regression equation is y = 14.374 - 0.145x Suppose the acyual completed entries per hour for an operator who is 35 years old was 8. The residual is:Heights (cm) and weights (kg) are measured for 100 randomly selected adult males, and range from heights of 137 to 192 cm and weights of 40 to 150 kg. Let the predictor variable x be the first variable given. The 100 paired measurements yield x = 167.80 cm, y = 81.45 kg, r=0.211, P-value = 0.035, and y = -103 +1.07x. Find the best predicted value of ŷ (weight) given an adult male who is 145 cm tall. Use a 0.01 significance level. The best predicted value of y for an adult male who is 145 cm tall is (Round to two decimal places as needed.) kg.Suppose an appliance manufacturer is doing a regression analysis, using quarterly time-series data, of the factors affecting its sales of appliances. A regression equation was estimated between appliance sales (in dollars) as the dependent variable and disposable personal income and new housing starts as the independent variables. The statistical tests of the model showed large t-values for both independent variables, along with a high r2 value. However, analysis of the residuals indicated that substantial autocorrelation was present.a. What are some of the possible causes of this autocorrelation?b. How does this autocorrelation affect the conclusions concerning the significance of the individual explanatory variables and the overall explanatory power of the regression model?c. Given that a person uses the model for forecasting future appliance sales, how does this autocorrelation affect the accuracy of these forecasts?d. What techniques might be used to remove this autocorrelation…