Two measures of a baseball players effectiveness as a hitter are the number of hits he makes in a season and the number of times he "bats in" a run (known as "runs batted in" or RBIS). Can we predict a batter's RBIS from his hits? Below is a numerical and graphical output from a computer regression of RBIS on Hits for 12 randomly selected Major League Baseball batters in 2017. Predictor Coef SE Coef T Constant 14.98 29.35 0.1915 0.51 0.621 Hits 0.3664 1.91 0.085 S = 14.359 R-Sq = 26.8% R-Sq (adj) = 19.5% Assume the conditions for inference have been met. a) Does these data provide convincing evidence that there is a linear relationship between RBIS and Hits for Major League Baseball batters in 2017? b) Construct a 95% confidence interval for the slope of the population regression line for predicting RBIS from hits.

Prehistoric pottery vessels are usually found as sherds (broken pieces) and are carefully reconstructed if enough sherds can be found. An archaeological study provides data relating x = body diameter in centimeters and y = height in centimeters of prehistoric vessels reconstructed from sherds found at a prehistoric site. The following Minitab printout provides an analysis of the data. Predictor Сoef SE Coef T P Constant -0.209 2.429 -0.09 0.929 Diameter 0.7689 0.1471 5.66 0.002 S 4.07980 R-Sq 88.9% %3D For the least-squares line ŷ = a + bx, what is the value of the constant a? What is the value of the slope b? (ote: The slope is the coefficient of the predictor variable.) Write the equation of the least-squares line. a = b = + The P-value for a two-tailed test corresponding to each coefficient is listed under P. The t value corresponding to the coefficient is listed under T. What is the P-value of the slope? Recall that the t value and resulting P-value of the slope b equal thet value…

Prehistoric pottery vessels are usually found as sherds (broken pieces) and are carefully reconstructed if enough sherds can be found. Information taken from a study provides data relating x = body diameter in centimeters and y = height in centimeters of prehistoric vessels reconstructed from sherds found at a prehistoric site. The following Minitab printout provides an analysis of the data. Predictor Coef SE Coef T P Constant -0.233 2.429 -0.09 0.929 Diameter 0.7948 0.1671 5.33 0.001 S = 4.10980 R-Sq = 80.3%       (a) The standard error Se of the linear regression model is given in the printout as "S." What is the value of Se?   (b) The standard error of the coefficient of the predictor variable is found under "SE Coef." Recall that the standard error for b is  Se   Σx2 −  1 n (Σx)2 .  From the Minitab display, what is the value of the standard error for the slope b?

A study was done to look at the relationship between number of movies people watch at the theater each year and the number of books that they read each year. The results of the survey are shown below.   Movies 10 7 6 10 0 9 1 6 Books 0 0 -0 0 9 0 9 -0 Use the model to predict the number of books read per year for someone who watches 3 movies per year.Books per year =  (Please round your answer to the nearest whole number.)   Interpret the slope of the regression line in the context of the question:   The slope has no practical meaning since people cannot read a negative number of books. As x goes up, y goes down. For every additional movie that people watch each year, there tends to be an average decrease of 0.98 books read. Interpret the y-intercept in the context of the question: The y-intercept has no practical meaning for this study. If someone watches 0 movies per year, then that person will read 8 books this year. The best prediction for a person who doesn't watch…