Applied Statistics: ANOVA and Multiple Regression Analysis

RUNNING HEADER: APPLIED STATISTICS 1
Applied Statistics
Students name:
Students ID:
Stat270/680

Applied Statistics 2
Question 1
a.
The hypothesis tests that can be used to determine if the depths of archeological discoveries vary
by site include ANOVA, linear regression and t-test.
b.
The hypothesis test chosen is ANOVA. The statistics tests was chosen since the data meets most
of the assumptions of an ANOVA test. The first and second assumption were met since the
dependent variable was continuous in nature while the independent variable was categorical in
nature.
> boxplot(Depth ~ Site, data = excavate)
From the boxplot above, it can be seen that there is constant variability between the sites. Thus,
there is independence of observation.
Consequently, the data was seen to be normally distributed as seen in the generated figure below:
> plot(depth.1, which = 1:2)

Applied Statistics 3
The only assumption that was violated was the absence of outliers. It was seen that there outliers
in the data as seen at point 36, 28 and 33.
c.
H0: The depths of the archeological discoveries do not vary by site
H1: The depths of the archeological discoveries vary by site
> View(excavate)
> depth.1 = lm(Depth ~ Site, data = excavate)
> anova(depth.1)
Analysis of Variance Table
Response: Depth
Df Sum Sq Mean Sq F value Pr(>F)
Site 3 2697.5 899.16 3.3514 0.02752 *
Residuals 43 11536.5 268.29
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Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
The computed test statistics from R programming is 3.3514. The null distribution for the test is
an F-distribution since it an F-test. Consequently, the p-value of the one-way ANOVA is
0.02752. Since the p-value is less than 0.05, we choose to reject the null hypothesis. Thus, it can
be concluded that the depths of the archeological discoveries vary by site. In addition, the result
is statistically significant.
Question 2
a.
The statistical model to be used will be:
batt_avg = c + runs + doubles + triples + home_runs + strike
b.
> plot(baseball)

Applied Statistics 4
Batt_avg correlated highly with runs but less with doubles and triples. Strike correlates
negatively with batt_avg and runs. Consequently, it can be seen that doubles weakly correlated
with triples. Low correlation among the variables make the variables suitable for a multiple
regression.
c.
> baseball.lm = lm(batt_avg ~ runs + doubles + triples + home_runs + strike, data =
baseball)
> summary(baseball.lm)
Call:
lm(formula = batt_avg ~ runs + doubles + triples + home_runs +
strike, data = baseball)
Residuals:
Min 1Q Median 3Q Max
-0.03970 -0.01143 -0.00101 0.01044 0.03444
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.18316 0.01714 10.685 3.79e-13 ***
runs 0.44668 0.10963 4.074 0.000219 ***