Chapter 8: Linear Regression—Part A. A.P. Statistics. Linear Model. Making a scatterplot allows you to describe the relationship between the two quantitative variables.
Allow us to make predictions and estimations about the population and future events.
It is a model of real data, as long as that data has a linear relationship between two quantitative variables.
Allows us to make predictions and estimations about the population and future events.
It is a model of real data, as long as that data has a nearly symmetric distribution.
“moving one standard deviation from the mean in x, we can expect to move about r standard deviations from the mean in y .”
LSRL of scatterplot:
For every standard deviation above (below) the mean a sandwich is in protein, we’ll predict that that its fat content is 0.83 standard deviations above (below) the mean.
Slope: One additional gram of protein is associated with an additional 0.97 grams of fat.
y-intercept: An item that has zero grams of protein will have 6.8 grams of fat.
ALWAYS CHECK TO SEE IF y-INTERCEPT MAKES SENSE IN THE CONTEXT OF THE PROBLEM AND DATA
The fact that the Sum of Squared Errors (SSE, same as Least Squared Sum)is as small as possible means that for this line:
Quantitative Variable Condition
Straight Enough Condition
with and without ?
What to Look for in a Residual Plot to Satisfy Straight Enough Condition:
No patterns, no interesting features (like direction or shape), should stretch horizontally with about same scatter throughout, no bends or outliers.
The distribution of residuals should be symmetric if the original data is straight enough.
Looking at a scatterplot of the residuals vs. the x-value is a good way to check the Straight Enough Condition, which determines if a linear model is appropriate.
* Calculate mean and standard deviation for each variable, if possible