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Chapter 4

STATS 10 Chapter Notes - Chapter 4: Batter Up, Scatter Plot, Dependent And Independent Variables


Department
Statistics
Course Code
STATS 10
Professor
Cha, M
Chapter
4

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Pratishta Natarajan
UID: 504786348
Section: 1A
Statistics Lab 2- Batter Up
1) I have attached the graph for at_bats and runs below:
       From the graph we can see that as the number of at_bats increases, the number of runs
increases as well. So this graph shows us that the relation is positive. Even though the graph
increases overall, it does not increase uniformly, ie: the variables are only moderately
correlated. So from this graph we can see that this variable not the most accurate to predict
the number of runs because we can only conclude that if the number of at_bats are higher,
the team’s runs are higher too. We cannot predict the exact number of runs a team would
score by only looking at the number of at_bats.
2)  I have attached the residual plot below:
The relationship between at_bats and run is linear. The plots are randomly scattered across
the horizontal axis. Therefore a linear model is more appropriate to represent the data.
In addition, the points do not form a “U” or and “Inverted U” shape. Therefore we can see
that a non-linear model would not be appropriate to explain the data.

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3) I have attached the graph for where I would put a single movable line, if I had to
summarize the graph. I have also added the “Sum of Squares” to it
The sum of squares is- 160600
Now I have attached two other graphs, that do not fit the data as well as the first graph does:
We can see that the sum of squares for these graphs are 201400 and 245400 respectively.
So we can see that the sum of squares reduces, and is the least when the line best fits the
data.
This is because the sum of squares is the square of the spread between each data point
from the mean. Since we are trying to find a line that fits the data the best, the spread needs
to be as little as possible. So the line of best fit will minimize the sum of squares. Which is
why the first graph has the least possible sum of squares for this data.
4) Below I have attached, the duplicate of the graphs I have used in the previous question. I
have changed the “Movable Line” to the “Least Squares Line”
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