Question

1. In 1994, baseball management and the players union failed to come to an agreement and the management initiated a work stoppage. The two sides did not come to an agreement until 1995. As a result less baseball games were played in both the 1994 and 1995 season. The 1994 and 1995 data seem to be outside the pattern of the rest of the data. Determine if these two data points are influential by:

a) Plot the regression line from the full data set on the on the scatter plot. The regression equation is: Wins = 24.5 + 0.08Runs, mark it “ALL SEASONS”

b) ​​​​​​​Plot the regression line from data set without the partial seasons on the on the scatter plot. The regression equation is: Wins = 43.3 + 0.05RUNS, mark it “ONLY FULL SEASON”. Do the partial seasons seem to be influential? Explain.

c) Using the linear regression model for “ALL GAMES” in the Red Socks data, Wins = 24.5+ 0.08 Runs. Consider the data for the year 2004, (Runs = 949, Wins = 98) Calculate the residual for this year.

d) The coefficient of determination = 67.2% for the Red Socks data. Find the linear correlation coefficient. Round your answer to 2 decimal places.

YEAR	GAMES PLAYED	RUNS	WINS
2009	162	872	95
2008	162	845	95
2007	162	867	96
2006	162	820	86
2005	162	910	95
2004	162	949	98
2003	162	961	95
2002	162	859	93
2001	161	772	82
2000	162	792	85
1999	162	836	94
1998	162	876	92
1997	162	851	78
1996	162	928	85
1995*	144	791	86
1994*	115	552	54
1993	162	686	80
1992	162	599	73
1991	162	731	84
1990	162	699	88

Answer 1

The regression lines for the two models “ALL SEASONS” and “ONLY FULL SEASON” are plotted in R. The screenshot is shown below,

R Code:

R Output:

a)

The model m1 is defined as,

Wins = 24.5 + 0.08Runs

The regression line is shown in red color in the scatterplot

b)

The model m2 is defined as,

Wins = 43.3 + 0.05RUNS

The regression line is shown in blue color in the scatterplot.

From the plot, we can see that the slope of the regression line is decreased which means the two data points are the influential data point.

c)

Residual = Actual - Predicted

The actual value of wins = 98,

The predicted is obtained from the regression model for runs = 949,

Wins = 24.5 + 0.08Runs

Wins = 24.5 + 0.08*949

Wins = 100.42

Residual = Actual - Predicted = 100 - 98 = 2

d)

The coefficient of determination, r^2 = 0.672

The correlation coefficient, r is