The following Minitab display gives information regarding the relationship between the body weight of a child (in kilograms) and the metabolic rate of the child (in 100 kcal/ 24 hr). Predictor       Coef         SE Coef          T               PConstant      0.8570         0.4148        2.06         0.84Weight         0.38243        0.02978     13.52       0.000 S = 0.517508      R-Sq = 97.4%   (a) Write out the least-squares equation. y^= ______ + _____x (b) For each 1 kilogram increase in weight, how much does the metabolic rate of a child increase? (Use 5 decimal places.)

The following table shows students’ test scores on the first two tests in an introductory physics class.  Physics Test Scores First test, x 7373 6161 6969 4242 8888 8787 4242 4444 4040 4848 6868 6464 Second test, y 7474 6262 6262 4343 7878 6969 3838 4343 3030 4848 6666 5454   Step 1 of 2 :   Find an equation of the least-squares regression line. Round your answer to three decimal places, if necessary.     Step 2 of 2 :  If a sudent scored a 75 on his first paper, make a prediction for his score on the second test. Assume the regression equation is appropriate for prediction. Round your answer to two decimal places, if necessary.

Table 14.17 The Least Squares Point Estimates for Exercise 14.51 Bo = 10.3676 (.3710) B1 = .0500 (<.001) B2 = 6.3218 (.0152) B3 = -11.1032 (.0635) B4 = -.4319 (.0002) Questions Using the t statistic and appropriate critical values, test Ho: βj = 0 versus Ha: βj ≠ 0 by setting α equal to .05. Which independent variables are significantly related to y in the model with α = .05? Using the t statistic and appropriate critical values, test Ho: βj = 0 versus Ha: βj ≠ 0 by setting α equal to .01. Which independent variables are significantly related to y in the model with α = .01? Find the p-value for testing Ho: βj = 0 versus Ha: βj ≠ 0 on the output. Using the p-value, determine whether we can reject Ho by setting α equal to .10, .05, .01, and .001. What do you conclude about the significance of the independent variables in the model? Calculate the 95 percent confidence interval for βj. Discuss one practical application of this interval. Calculate the 99 percent confidence interval for…