Chapter 7 and 8
What does a negative residual mean
A predicted value is too big (an overestimate)
What does a positive residual mean
A predicted value is too small (an underestimate)
What is a plot of residuals important for showing
Identifying if there is a curved relationship or not
A straight line can almost never go through all the data points exactly in a scatter plot, but how can a straight line help us
It can help us understand how the variable are associated
What does R squared represent in linear regression
It gives the fraction for the data's variance accounted for by the model
What does it mean when a point is said to be influential
It is influential if omitting it from the analysis gives a very different model
What does an R squared that equals 1 indicate
It means that all of the variability in the data is explained by the model (it is always between 0 and 1, or 0 and 100%)
What does an R squared that equals 0 indicate
It means that none of the variability in the data is explained by the model (it is always between 0 and 1, or 0 and 100%)
If a residual chart is linear, what does that mean
That the relationship is curved (a residual chart should show no relation and look boring)
What two things are the slope based on in statistics
The correlation and the standard deviation (standard deviation is always positive) (if the correlation is positive there will be a positive slope, and vice versa)
What is a linear model
The equation of a straight line through the data
What does a linear value with smaller residual values mean
The line fits better in the plot
What is the least squares line (best fit line)
The line that best fits through the data where the sum of the squares of the residuals is the smallest
What does it mean when a point has high leverage
The point lies far from the mean of the x values
What is the estimate of a linear value on a scatterplot called
The predicted value (called y hat)
What is the difference between the predicted and observed value called
The residual value (predicted value-observed value)
What is bsub1
The slope (tells us how rapidly y hat changes in respect to x)
What is bsub0
The y intercept (tells us where the line crosses the y-axis)
True or false: a model with the same magnitude of correlation, even in opposite directions, will have the same r squared
True (it will always be positive because it is squared)
What are the units of the slope
Units of y per units of x (y over x)
When is it inappropriate to use a regression line
When comparing two categorical values, when there are outliers, and when there isn't a straight relationship (the relationship has no correlation or it is curved)
How is the equation for a straight line (y=mx+b in algebra) written in statistics
y hat=bsub0+bsub1*x
