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