AP Stats Chapter 3 Test

Which of the following statements are true about the least-squares regression line? 1.) the slope is the predicted change in the response variable associated with a unit increase in the explanatory variable 2.) The line always passes through the point (x,y), the means of explanatory and response variables 3.) It is the line that minimizes the sum of the squared residuals

1, 2, and 3 are all true

Which of the following statements about influential points and outliers are true? 1.)An influential point always has a high residual 2.)Outliers are always influential points. 3.) Removing an influential point always causes a marked change in either the correlation, the regression equation, or both.

3 only

Suppose we fit the least-squares regression line to a set of data. If a plot of the residuals shows a curved pattern...

A straight line is not a good summary for the data

The correlation between mid-Aught and soil moisture and the per-acre yield of tomatoes is r=0.53

Not correct, and contains an error

You are examining the relationship between x= the height of red oak trees and y=the number of acorns You calculate a correlation coefficient and a least-squares regression line. If you switched the variables (that is, let x = number of acorns and y= height of trees), which of the following would be true?

The correlation coefficient would not change, but the regression line would change.

Which of the following describes what the number S=3.376 represents?

The standard deviation of the residuals is 3.376

Which of the following best describes what S=10.537 represents in this setting

This represents the average of the products of each standardized value for height and the corresponding standardized value for speed.

when given values to calculated the least-squares regression line:

b=r(sy/sx) a=y_-bx_

a ... in regression is any point that, if removed, substantially changes the slope, y-int, correlation, coefficient of determination, or standard deviation of the residuals

influential point

correlation and regression lines describe only

linear relationships

Correlation and least-squares regression lines are

not resistant

A ... is regression is a point that does not follow the pattern of he data and has a large residual

outlier

What is the sum of the residuals equation?

s=v/(sum of (yi-y^i)^2)/(n-2)

correlation is r^2...

square rooted to get r

the least lines regression model will go from slanted to...

straight across with a similar shape in data

Points in regression have much larger or much smaller x-values than the other points in the data set...

with high leverage

What part of the graph is the explanatory variable

x-axis

What part of the graph is the responsive variable

y-axis

Calculate residual

y-ŷ

What do you do after solving for y^ to get to r?

y^-y=r

Least squares regression line equation

y^=a+bx