A statistical program is recommended. Consider the following data for a dependent variable y and two independent variables, x, and x2. 30 12 94 47 10 108 25 17 112 51 16 178 40 5 94 51 19 175 74 7 170 36 12 11 7 59 13 142 76 16 211 The estimated regression equation for the data is i --18.4 + 2.01x, + 4.74x2- (a) Develop a 95% confidence interval for the mean value of y when x, - 51 and x, = 19. (Round your answers to three decimal places.) to (b) Develop a 95% prediction interval for y when x - 51 and x, - 19. (Round your answers to three decimal places.) to
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- The following data are the monthly salaries and the grade point averages for students who obtained a bachelor's degree in business administration. GPA Monthly Salary ($) 2.6 3,600 3.4 3,900 3.6 4,300 3.2 3,800 3.5 4,200 2.9 3,900 The estimated regression equation for these data is and . Use Table 1 of Appendix B. a. Develop a point estimate of the starting salary for a student with a GPA of (to 1 decimal). b. Develop a confidence interval for the mean starting salary for all students with a GPA (to 2 decimals). ( , ) c. Develop a prediction interval for Ryan Dailey, a student with a GPA of (to 2 decimals). ( , ) d. Discuss the differences in your answers to parts (b) and (c).Use the following information from a multiple regression analysis. n=15 b1=2 b2=6 Sb1=1.4 Sb2=0.5 a. Which variable has the largest slope, in units of a t statistic? b. Construct a 90% confidence interval estimate of the population slope, β1. c. At the 0.10 level of significance, determine whether each independent variable makes a significant contribution to the regression model. On the basis of these results, indicate the independent variables to include in this model.Given below are seven observations collected in a regression study on two variables, x (independent variable) and y (dependent variable). Copy and paste the numbers in an Excel worksheet and then use Excel's Regression tool to conduct a simple linear regression analysis. Choose 95% confidence level. Answer the following questions: x y 2 12 3 9 6 8 7 7 8 6 7 5 9 2 Find out regression coefficient b1 (Keep 2 decimal places) Find out SSR (Keep 2 decimal places) Find out SST (Only report the integer part)
- For each of the following scenarios, select the test (from the choices below), that is most appropriate for analyzing the data. a) Z-test b) One-sample t-test c) Independent t-test d) Dependent t-test e) 1-Way ANOVA f) Regression/Correlation g) Chi-Square 1. Does caffeine help test performance? 90 participants are randomly assigned to one of 4 groups (no caffeine, small dose, medium dose, and large dose) and then asked to complete a GRE math section. 2. Do seniors study for fewer hours per week than freshmen? 3. Is the average SAT math score of Hunter College students higher than the national average (μ = 500, σ = 100)?Given below are seven observations collected in a regression study on two variables, x (independent variable) and y (dependent variable). Copy and paste the numbers in an Excel worksheet and then use Excel's Regression tool to conduct a simple linear regression analysis. Choose 95% confidence level. Answer the following questions: x y 2 12 3 9 6 8 7 7 8 6 7 5 9 2 t statistics is statistically significant at 5% level. Answer Yes or No. Yes No What is the lower bound of the 95% confidence interval for the independent variable x (Keep 2 decimal places) What is the upper bound of the 95% confidence interval for the independent variable x (Keep 2 decimal places)Given below are seven observations collected in a regression study on two variables, x (independent variable) and y (dependent variable). Copy and paste the numbers in an Excel worksheet and then use Excel's Regression tool to conduct a simple linear regression analysis. Choose 95% confidence level. Answer the following questions: x y 2 12 3 9 6 8 7 7 8 6 7 5 9 2 Find out F Statistics (Only report the integer part) F Statistics is statistically significant at 5% level. Answer Yes or No. Yes No Find out t statistics for the independent variable x (Keep 2 decimal places) t statistics is statistically significant at 5% level. Answer Yes or No. Yes No What is the lower bound of the 95% confidence interval for the independent variable x (Keep 2 decimal places) What is the upper bound of the 95% confidence interval for the independent variable x (Keep 2 decimal places)
- Consider the following set of dependent and independent variables. Use these data to answer questions a and b in the photos below. y 47 44 40 40 27 21 19 15 9 x1 22 32 18 19 10 18 8 15 9 x2 71 60 81 55 42 46 32 17 16 a) construct a 95% confidence interval for the regression coefficient for x1 and interpret its meaning. -the 95% confidence interval for the true population b1 is ___ to ___. b) Construxt a 95% confidence interval for the regression coefficient for x2 and interpret its meaning. -the 95% confidence interval for the true population coefficient b2 is ___ to ___. Please help!!In exercise 12, the following data on x = average daily hotel room rate and y = amount spent on entertainment (The Wall Street Journal, August 18, 2011) lead to the estimated regression equation ŷ = 17.49 + 1.0334x. For these data SSE = 1541.4. Use Table 1 of Appendix B.Click on the datafile logo to reference the data. 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 $89 (to 2 decimals).$ to $ c. The average room rate in Chicago is $128. Develop a 95% prediction interval for the amount spent on entertainment in Chicago (to 2 decimals).$ to $Suppose you estimated the relationship between the exam scores and class sizes. score^ = b0 + b1*Size + e^ Based on the OLS estimate, you obtain the following standard errors and parameter estimates: b0= 95; se(b0) = 30 ; b1= −1.2; se(b1 ) = 0.4 ; n = 25 a) What kind of relationship exist between the exam scores and the clas sizes? Interpret the regression. b) Conduct the following hypothesis test at the 1% significance level: H0 : b1 ≥ 0 H1 : b1 < 0 In your answer draw the distribution of the test statistic that you use, and clearly define the rejection region(s), indicating the critical value(s).
- In exercise 12, the following data on x = average daily hotel room rate and y = amount spent on entertainment (The Wall Street Journal, August 18, 2011) lead to the estimated regression equation ŷ = 17.49 + 1.0334x. For these data SSE = 1541.4.Click on the datafile logo to reference the data. 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 $89 (to 2 decimals).$ to $ 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).WHat is the confidence interval? Consider the following data on x = rainfall volume (m3) and y = runoff volume (m3) for a particular location. x 5 12 14 18 23 30 40 46 55 67 72 83 96 112 127 y 4 10 13 14 15 25 27 45 38 46 53 71 82 99 105 Use the accompanying Minitab output to decide whether there is a useful linear relationship between rainfall and runoff. The regression equation isrunoff = -2.05 + 0.847 rainfall Predictor Coef Stdev t-ratio p Constant -2.049 2.251 -0.91 0.379 rainfall 0.84717 0.03465 24.45 0.000 s = 4.978 R-sq = 97.9% R-sq(adj) = 97.7% State the appropriate null and alternative hypotheses. H0: β1 = 0 Ha: β1 ≠ 0 H0: β1 ≠ 0 Ha: β1 = 0 H0: β1 = 0 Ha: β1 < 0 H0: β1 = 0 Ha: β1 > 0 Compute the test statistic value and find the P-value. (Round your test statistic to two decimal places and your P-value to three decimal places.) t = P-value = State the conclusion in the problem context. (Use α = 0.05.) Reject H0. There…Suppose we are making predictions of the dependent variable y for specific values of the independent variable x using a simple linear regression model holding the confidence level constant. Let Width (C.I) = the width of the confidence interval for the average value y for a given value of x, and Width (P.I) = the width of the prediction interval for a single value y for a given value of x. Which of the following statements is true? Width (C.I) = 0.5 Width (P.I) Width (C.I) = Width (P.I) Width (C.I) > Width (P.I) Width (C.I) < Width (P.I)