1. Ch 4.1 & 4.2 Two dimensions concept
I. Scatter plot

2. exponential regression
linear regression
quadratic regression
power regression
exponential regression
Linear Regression
perfect correlation
positive correlation
negative correlation
no correlation
As x increases, y increases
As x increases, y decreases

3. II. Correlation coefficient (r)
1. Covariance between X and Y
The covariance is a measure of how two variables vary together.
2. When = 0, there is no correlation.
If is large, it is difficult to interpret.
Pearson used a formula to standardize the covariance, which is called the Pearson Correlation Coefficient .
where is the sample standard deviation of the explanatory variable x.
where is the sample standard deviation of the response variable y.

4. 3. r measures the strength of the linear association between X and Y.
r = -1
r = 0
r = 1
perfect negative correlation
no correlation
perfect positive correlation
If > the critical value for Correlation Coefficient obtained from Table II, there is a positive/negative linear correlation between X and Y.

5. III. Least-Squares Regression Line
If there is positive/negative correlation between X and Y, find the best fitted line for the data.
The least-square regression line, , is the line that minimizes the sum of the squared errors (residuals).
Residual = observed y – predicted y

6. The least squares regression line is
where
is the slope of the least-squares regression line
and
is the y-intercept of the least-squares regression line

7. Summary:
1. Use StatCrunch to plot a scatter plot
2. Use StatCrunch to calculate r
3. Determine whether there is a positive/negative linear correlation between X and Y.
If > the critical value for Correlation Coefficient obtained from Table II, there is a positive linear correlation between X and Y for r is positive and there is a negative linear correlation between X and Y for r is negative.
4. If there is a linear correlation between X and Y, use StatCrunch to find the least squares regression line Otherwise, do not find the least squares regression line.

8. When a value is assigned to X  if there is a correlation between X and Y, use the least squares regression line to find the best predicted Y.
When a value is assigned to X  if there is no correlation between X and Y, use StatCrunch to find and the best predicted Y is for any X.