Question

1. The following table gives data on the Boston Red Sox wins and runs. Construct a scatterplot with runs on the horizontal axis and wins on the vertical axis.

a) Do you think there is a linear relationship between the number of runs and the number of wins in a given year?

b) The linear regression line for the data is: Wins = 24.5+ 0.08 Runs. Use this model to predict the number of wins the Red Socks would have in a season where they had 800 Runs. (Round your answer to one decimal place)

c) What is the slope of the regression line? Interpret the slope.

d) What is the y-intercept of the regression line? Can you interpret the y-intercept? Why or why not? If you can, do so.

RUNS	WINS
872	95
845	95
867	96
820	86
910	95
949	98
961	95
859	93
772	82
792	85
836	94
876	92
851	78
928	85
791	86
552	54
686	80
599	73
731	84
699	88

Answer 1

The given information is related to Boston Red Sox wins and runs. Follow the below steps to construct the scatter plot using Excel: 1. Enter the given data in Excel spread sheet. 2. Select the data. 3. Select Insert, Scatter, Scatter with only Markers. The output displayed as given below:

Wins 0 200 400 600 800 1000 1200 Runs

(a) Yes, there is a linear relationship exists between the number of runs and the number of wins in a given year. From the Scatter plot, it is observed that there is increasing tendency present in the data. Therefore, there is a linear relationship exists between the number of runs and the number of wins in a given year. (b) From the given information, the regression line is Wins = 24.5 +0.08 Runs. The objective is to predict the number of wins the Red Socks would have in a season where they had 800 Runs Substitute the Runs value as 800 in regression line.

Wins = 24.5+0.08 Runs Wins = 24.5+0.08(800) Wins = 88.5 Therefore, the number of wins the Red Socks would have in a season where they had 800 Runs is 88.5. From the known information, the general form of the simple linear regression equation is, y = Bo + Bx Here, B. is the intercept of the regression line, B is the slope of the regression line, x is the independent variable, y is the dependent variable. After comparing the general form of the simple linear regression equation with given regression equation,

The slope of the regression line is 0.08. Interpretation: If one unit change in Runs 0.08 times change will be occurred in Wins while keeping all the other variables as constant. After comparing the general form of the simple linear regression equation with given regression equation, The y-intercept of the regression line is 24.5. No, it is not possible to interpret the y-intercept because there is no meaning for the interpretation keeping runs as a constant. That means, without having runs the game is not going to win.