Stats 50 Ch. 10.3

Front 1

The best fitting straight line that describes the relationship between x and y is called:

Back 1

regression line

Front 2

The equation for the regression line is called:

Back 2

The regression equation

Front 3

The regression equation is:

Back 3

ŷ = ax + b

Front 4

The regression equation algebraically describes:

Back 4

the relationship between the two variables x and y.

Front 5

The graph of the regression equation is called:

Back 5

the regression line, or line of best fit, or least-squares line.

Front 6

The regression equation expresses a relationship between:

Back 6

x and ŷ

Front 7

Requirements for finding the equation of a regression line:

Back 7

1) Sample of paired (x,y) data is a simple random sample.
2) Scatterplot confirms that points approximate a straight-line pattern.
3) Outliers are removed if they are errors.

Front 8

Use the regression equation for predictions only if:

Back 8

1) scatterplot confirms regression line fits points well.
2) r indicates there is a strong linear correlation.
3) The prediction is not beyond the scope of the avail. sample data.

Front 9

The best predicted value of a variable is:

Back 9

its point estimate, which is its sample mean.

Front 10

If using the regression equation to predict a value of y when given some value of x:
1) If the regression equation is a good model:
2) If the regression equation is not a good model:

Back 10

1) If the regression equation is a good model: substitute a value of x into the regression equation to find the predicted value of y.
2) If the regression equation is not a good model: the best predicted value of y is simply y̅, the mean of the y values.

Front 11

In working with two variables related by a regression equation, the marginal change in a variable is:

Back 11

the amount that it changes when the other variable changes by exactly one unit.

Front 12

The slope in the regression equation represents the marginal change in:

Back 12

y that occurs when x changes by one unit.

Front 13

In a scatterplot, an outlier is:

Back 13

a point lying far away from the other data points.

Front 14

Paired sample data may include one or more influential points, which are:

Back 14

points that strongly affect the graph of the regression line.

Front 15

A point is an influential point if:

Back 15

the graph of the regression line changes by a considerable amount if it is graphed again with the point excluded.

Front 16

ŷ represents:

Back 16

the predicted y value

Front 17

The regression equation represents a straight line that best fits the data. The criterion to determine the line that is better than all others is based on:

Back 17

the vertical distances between the original data points and the regression line. Such distances are called residuals.

Front 18

For a pair of sample x and y values, the residual is:

Back 18

the difference between the observed sample value of y and the value of y predicted using the regression equation.

Front 19

residual =

Back 19

observed y − predicted y
y − ŷ

Front 20

The regression equation represents the line that "best" fits the points according to:

Back 20

the least-squares property.

Front 21

A straight line satisfies the least-squares property if:

Back 21

the sum of the squares of the residuals is the smallest sum possible.

Front 22

What equation represents the least-squares property:

Back 22

∑(y − ŷ) = smallest sum possible

Front 23

Define extrapolation:

Back 23

Extrapolation is trying to predict the value of y when the value of x is out of the range of the sample x-values.