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

_____________________ is the use of a regression line for prediction outside the interval of x values used to obtain the line.

To make a prediction using the regression line, you would...

• plug in a predicted guess for y-hat and simplify

• look at the scatterplot

• rearrange the equation to solve for x

• plug in a value for x and simplify

Tags

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.

Standard deviation of residuals s...

• The standard deviation of the residuals s measures the size of a typical residual.

• $s=\sqrt{\frac{sum\ of\ squared\ residuals}{n-2}}$

• $s=\sqrt{\frac{\sum_{ }^{ }\left(y_i-y_i^{\wedge}\right)^2}{n-2}}$

• That is, s measures the typical distance between the actual y values and the predicted y values.

Tags

CCSS.HSS.ID.B.6