Applied Statistics: Analysis of Scatter Plot, Correlation Coefficient, Regression Model, Confidence Interval, and Coefficient of Determination

APPLIED STATISTICS
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Question 1
The relevant scatter plot between the given variables is shown below.
Based on the above scatter plot, it is apparent that there is a positive slope for the best fit line
which is sloping upwards. This clearly represents that the direction of relationship between the
given variables is positive. As a result, it would be expected that golfers who had high score with
the original clubs would also have high scores when using the new clubs. The strength of the
relationship between the scores seems to be moderately strong as the deviation of the scatter
points from the line of best fit does not seem to be high.
Question 2
The correlation coefficient between the given variables is shown below.

The correlation coefficient has come out to be positive which is consistent with the positive slope
of the line of best fit which was represented in the above scatterplot. With regards to the strength,
it is noteworthy that the correlation coefficient would vary between 0 and 1 in terms of value.
Considering that the correlation coefficient is quite close to 1, hence the analysis in the previous
case based on the scatterplot was correct. It can be concluded that the correlation coefficient
between the given variables hints at positive and moderately strong linear relationship.
Question 3
(a) Regression model
Least Square Regression Line
New Score=4.658+(0.909∗Old Score)
(b) Slope coefficient = 0.909
The slope coefficient comes out to be 0.909 which implies that for a unit increase in the old score
would increase the new score by 0.909 units.