least squares regression line

Y-hat is the ________ value of y for a given value of x.

Tags

CCSS.HSF.IF.A.1

CCSS.HSF.IF.A.2

What is the formula for the regression line?

• y=mx+b

• 
  

  $y^{\wedge}=ax+b$

• y=a+bx

• $y^{\wedge}=a+bx$

Tags

CCSS.HSA.CED.A.2

CCSS.HSS.ID.C.7

A residual...

• the difference between the actual value of y and the value of y predicted by the regression line

• actual y - predicted y

• $y-y^{\wedge}$

• the difference between the actual value of x and the value of x predicted by the regression line

In the regression equation ˆy=a+bx:

• When asked to interpret the slope or y intercept, it is very important to include the word predicted (or equivalent) in your response.

• a is the y-intercept

• using the regression line to make a prediction for x=0 is an extrapolation

• b is the slope, the amount by which the predicted value of y

  changes when x increases by 1 unit

Tags

CCSS.HSS.ID.C.7

A ______________ regression line makes the residuals as small as possible.

• good

• bad

• ugly

• mean

A ______________ plot is a scatterplot that displays the residuals on the vertical axis and the explanatory variable on the horizontal axis.

• residual

• predicted

• estimated

• left overs

To determine whether the regression model is appropriate, look at the residual plot.

• If there is no leftover curved pattern in the residual plot, the regression model is appropriate.

• If there is leftover curved pattern in the residual plot, the regression model is appropriate.

• If there is a leftover curved pattern in the residual plot, consider using a regression model with a different form.

• If there is not a leftover curved pattern in the residual plot, consider using a regression model with a different form.

The ___________________ measures the percent of the variability in the response variable that is accounted for by the least-squares regression line.

• coefficient of determination

•  $x^2$  

•  $r^2$  

• coefficient of relaxation

Tags

CCSS.HSS.ID.C.8

Which of the following definitions are true...

• Points with high leverage in regression have much larger or much smaller x values than the other points in the data set.

• An outlier in regression is a point that does not follow the pattern of the data and has a large residual.

• An influential point in regression is any point that, if removed, substantially changes the slope, y intercept, correlation, coefficient of determination, or standard deviation of the residuals.

• All of the above

Tags

CCSS.HSS.ID.A.3

You are analyzing a scatter plot that has a negative correlation. What is true of the of the x and y values?

• As x increases, y decreases
• As x increases, y increases
• As x decreases, y decreases

Tags

CCSS.HSS.ID.B.6

CCSS.HSS.ID.C.8