Honors Stats2 Day 5
Do Now
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There is a moderately strong positive
correlation (0.62) between male’s height
and salary.
1) What does that mean?
2) If Alfonso (75in) wants to predict his
salary knowing that the average male
height is 69in with an SD of 2.9in and the
average male(age 25-35) salary is
$40,650 with a SD of $10,520, what
would his salary be?
Interpretation
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Correlation(r): as one variable goes
up, what happens to the other
Slope: for every change of 1 x, there
is m amount of change in y
Y-Intercept: the starting point (x=0)
R squared
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Literally squaring the “r” term
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Interpreting R Squared
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Change R2 into a percent
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R2% of variation in y is explained by
variation in x.
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Practice:
There is a strong negative correlation (0.76) between age and electronics
purchases. Interpret R2
• Interpret the correlation and the following
line of best fit that describes the
correlation that predicts the age of a
person.
• ^
y = -13x + 83
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Practice Interpreting
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Worksheet
What was residual
again?
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Observed value - Predicted value
Example 1: According to the correlation between
absences and quiz grades, Rico was predicted to score
an 80 on his quiz. He scored an 82. What was the
residual?
Example 2: According to the correlation between age
and spending, I was predicted to spend $737/mo at
my age. I actually spent $722. What was the
residual?
More Examples
Given the graph, approximate the
residual for…
1) 4 hours worked?
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2) 1 hour worked?
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More Examples
Given that the line of best fit is
• 32.4x+5 and the actual value for 4
was 123, what is the residual value?
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Residuals
Tell us how well the model/line fits!
• (is the line “appropriate”)
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If a model makes sense, it should
show us the underlying relationship–
the leftovers should show nothing (no
association)
Plotting Residual
Testing for Fitness
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After making a regression line, plot
the residuals and hope for NOTHING
If this is your
residual plot…
Residual Exit Ticket
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You have just completed Unit 2 on
Correlation and Linear Regression
Homework
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Chapter 8 #3, 4, 9, 10, 13, 14, 27