Analysis of Ice Thrust, Muzzle Velocities and Coconut Palm Production using Statistics

RESEARCH METHODS: CRASH COURSE IN STATISTICS
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Section B:
1.
a. Ice thrust was found to be positively depending on ship speed with a high significant
positive correlation. The trend indicated a sharp rise in ice thrust along a positive direction
for increase in ship speed. For low speed of 3 meters/second or less very less ice thrust was
observed. Once the ship speed increased to 4 meters/second and above the ice thrust was
noted to range above 250 thousands Newtons. Maximum thrust was observed for ship speed
of 7 meters/second.
876543210
500
400
300
200
100
Ship_speed (Meters/Second)
Ice_Thrust (In thousand Newtons)
Ice Thrust Dependence on Ship Speed
For K1=35
b. The Pearson’s correlation coefficient for the association of ice thrust and ship speed was
found to be positive and significant ( R=0. 87 , p<0 . 05 ).
The correlation value was in line with the trend of the scatter plot of ice thrust and ship
speed, where the positive correlation was evident from the plot.
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The corresponding null hypothesis assumed was that there was no correlation between ice
thrust and speed of ship. The hypothesis was tested at 5% level of significance and the test
statistic of Pearson’s correlation ( R=0. 87 , p<0 . 05 )signified that there was a significant
correlation different from zero at 55 level of significance.
c. The linear regression model was constructed in MINITAB with Ice thrust as the response
variable and ship speed as the predictor variable. The model was found to be statistically
significant ( F=87 . 49 , p<0 . 05 ) at 5% level of significance. The estimated regression
equation was identified as IceThrust =145 . 0+ 40 . 28∗ShipSpeed . Hence, for increase in
ship speed for 1 meter/second the thrust of ice was observed to increase by 40.28 thousand
Nektons. The coefficient of determinant or the R-square implied that ship speed was able
to explain 75.76% variation in thrust of ice. The inclusion of adjusted R-square indicated
that the prediction for the variation in response variable was 74.89% for inclusion of the
predictor variable and the predicted R-square was even smaller than the adjusted R-square.
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d. The null hypothesis for the slope of the regression estimating the population slope was that
there was no linear relation between the response and predictor variable as H 0 : ( β=0 ) . The
null hypothesis was tested at 5% level of significance against the two tailed alternate
hypothesis( HA : β≠0 ) . The t-test statistic was evaluated as t=40. 28−0
4 . 31 =9. 35 and the p-
vale was calculated as P (|t|>9 . 35 ) =0 . 000 at 29 degrees of freedom at 5% level of
significance. The results indicated that the p-value was less than alpha value of 0.05, and
hence the null hypothesis was rejected at 5% level. Therefore, it was inferred that ice thrust
and ship speed had significant positive linear association between them.
e. The residual plot revealed that the residuals were aligned along the fitted distribution line.
The points or residuals in the following plot were well within the vicinity of the fitted line
and the distribution seems to be a good fit for the regression analysis.
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