1. The Weather Turbulence
Unit 4 – Bivariate Data
12/6/2018
Algebra 1 Institute

2. Could a city’s elevation above sea level be used to predict the number of cloudy, partly cloudy, or clear days per year a city experiences?
12/6/2018
Algebra 1 Institute

3. Scatterplot
Do you see a pattern in the scatter plot, or does it look like the data points are scattered?
How would you describe the relationship between elevation and mean number of clear days for these 14 cities? That is, does the mean number of clear days tend to increase as elevation increases, or does the mean number of clear days tend to decrease as elevation increases?
Do you think that a straight line would be a good way to describe the relationship between the mean number of clear days and elevation? Why do you think this?
12/6/2018
Algebra 1 Institute

4. How Strong is the Pattern?
Correlation Coefficient
The value of the correlation coefficient ranges between –1 and +1.
The greater the absolute value of a correlation coefficient, the stronger the linear relationship.
12/6/2018
Algebra 1 Institute

5. How Strong is the Pattern?
Correlation Coefficient
The strongest linear relationship is indicated by a correlation coefficient of –1 or +1.
The weakest linear relationship is indicated by a correlation coefficient equal to 0.
A positive correlation means that if one variable gets bigger, the other variable tends to get bigger.
A negative correlation means that if one variable gets bigger, the other variable tends to get smaller.
12/6/2018
Algebra 1 Institute

6. 12/6/2018
Algebra 1 Institute

7. Calculate the Correlation Coefficient
where is the deviation score and
is the sample mean
(Software!)
12/6/2018
Algebra 1 Institute

8. Coefficient of Determination – R2
The coefficient of determination is the square of the correlation coefficient
R2 = r2
The correlation coefficient ranges from –1 to +1.
So the coefficient of determination ranges from 0 to +1.
12/6/2018
Algebra 1 Institute

9. Coefficient of Determination – R2
X = independent variable (predictor)
Y = dependent variable (response)
An R2 of 0 means that X does not explain any of the variation in Y.
An R2 of 1 means X explains all the variation in Y.
Intermediate values: an R2 between 0 and 1 indicates the extent to which Y is explained by X
R2 of 0.10 means that 10 percent of the variation in Y is explainable from X
R2 of 0.20 means that 20 percent is explained; and so on.
12/6/2018
Algebra 1 Institute
12/6/2018
Algebra 1 Institute 9

10. The Least Squares Regression Line
ŷ = b0 + b1x
Where b0 is an estimate of the intercept
b1 is the estimate of the slope
b0 and b1 are regression coefficients
x is the value of the independent variable,
ŷ is the predicted (fitted) value of the dependent variable.
12/6/2018
Algebra 1 Institute

11. The Least Squares Regression Line
Estimates: or
where
and
(Software!)
12/6/2018
Algebra 1 Institute

12. The Least Squares Regression Line
Estimates:
12/6/2018
Algebra 1 Institute

13. The Weather Turbulence
Construct a scatter plot that displays the data for
x = elevation above sea level (in feet), and,
w = mean number of partly cloudy days per year
Based on the scatter plot you constructed,
Is there a relationship between elevation and the mean number of partly cloudy days per year?
If so, how would you describe the relationship?
Explain your reasoning.
12/6/2018
Algebra 1 Institute