Regression Analysis and Hypothesis Testing in Statistics

STATISTICS
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Question 1
(a) Scatter plot
Dependent variable: Team winning %
Independent variable: Team batting average
0.245 0.25 0.255 0.26 0.265 0.27 0.275 0.28 0.285
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f(x) = 2.98984526112185 x − 0.284358317214699
R² = 0.241477813185592
Scatter Plot
Team Batting Average
Team Winning %
It is apparent from the positive slope of the best fit line that there is a positive correlation
between the given variables. However, considered that the points have significant deviation from
the best fit line, it is apparent that the correlation is weak to moderate only and not strong (Flick,
2015).
(b) Correlation coefficient is calculated though CORREL () function of excel and is shown
below.

(c) Coefficient of determination R2 = (Correlation coefficient)2 = (0.4914)2 = 0.2415
Coefficient of determination indicates that 24.15% of the variation in the dependent variable
(team winning percentage) can be explained by the variation in the independent variable (team
batting average) (Hillier, 2016).
(d) Sample regression line can be found through the regression model as shown below.
Regression equation
Team winning %=−0.2844 + ( 2.9898∗Team Batting Average )
Intercept: The value of intercept indicates that the team winning percentage would be -0.2844
when the team batting average comes out to be zero. Hence, the team winning percentage is not
practical as the team winning percentage cannot be negative.
Slope coefficient: The value of slope coefficient indicates that when the team batting average is
increased by one unit then the team winning percentage would be increased by 2.9898%.
(e) Level of significance = 5%