Question

Here is the data Stat7_prob2.txt :

"Team","WINS","HR","BA","ERA"
"Anaheim Angels",99,152,.282,3.69
"Baltimore Orioles",67,165,.246,4.46
"Boston Red Sox",93,177,.277,3.75
"Chicago White Sox",81,217,.268,4.53
"Cleveland Indians",74,192,.249,4.91
"Detroit Tigers",55,124,.248,4.93
"Kansas City Royals",62,140,.256,5.21
"Minnesota Twins",94,167,.272,4.12
"New York Yankees",103,223,.275,3.87
"Oakland Athletics",103,205,.261,3.68
"Seattle Mariners",93,152,.275,4.07
"Tampa Bay Devil Rays",55,133,.253,5.29
"Texas Rangers",72,230,.269,5.15
"Toronto Blue Jays",78,187,.261,4.8
"Arizona Diamondbacks",98,165,.267,3.92
"Atlanta Braves",101,164,.26,3.13
"Chicago Cubs",67,200,.246,4.29
"Cincinnati Reds",78,169,.253,4.27
"Colorado Rockies",73,152,.274,5.2
"Florida Marlins",79,146,.261,4.36
"Houston Astros",84,167,.262,4
"Los Angeles Dodgers",92,155,.264,3.69
"Milwaukee Brewers",56,139,.253,4.73
"Montreal Expos",83,162,.261,3.97
"New York Mets",75,160,.256,3.89
"Philadelphia Phillies",80,165,.259,4.17
"Pittsburgh Pirates",72,142,.244,4.23
"St. Louis Cardinales",97,175,.268,3.7
"San Diego Padres",66,136,.253,4.62
"San Francisco Giants",95,198,.267,3.54

Here is the question:

Please Use R software/studio and provide all the R code and R output, please. Please answers all the questions (a, b, c, d, e, f & g). Pay attention to everything in Bold please. Show all work!

The file Stat7_prob2.txt contains data on the following variables for the 30 major league base- ball teams during the 2002 season:

• WINS: number of games won
• HR: number of home runs hit
• BA: average batting average
• ERA: earned run average

(a) Using WINS as the dependent variable, run the regression relating the three predictor variables to WINS. Reportthe fitted regression line.

(b) Construct the ANOVA table of the above model.

(c) Plot the residuals e against the fitted values y^i . What departures from the regression model assumptions can be studied from this plot? What are your findings? (Note: If you are not sure about the validity of any of the assumptions, perform a formal test to verify your answer.)

(d) Prepare a normal probability plot (QQ plot) of the residuals. Which assumption can be tested from this plot and what do you conclude? (Note:You can also use the formal test to reinforce your conclusion).

(e) If there is no problem with any of the assumptions, you can safely continue with making inference. Test for the significance of the regression using a 0.05 significance level.

(f) What percentage of the variability in y is explained by the regression?

(g)Using the individual t-tests, comment on the significance of each predictor variable, using a 0.05 significance level.

Answer 1

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