Regression

Question 1

What is the explanatory variable?

Answer 1

The independent variable = the one that is set independently of the other variable.

It is plotted along the x-axis

Question 2

What is the response variable?

Answer 2

The dependent variable = the one whose values are determined by the values of the independent variable.

It is plotted along the y-axis

Question 3

What is the equation of a straight line?

Answer 3

y = a + bx

Where b = Sxy / Sxx

And a = mean of y - b(mean of x)

Question 4

When can the straight line equation y = a + bx be used as a model for a relationship?

Answer 4

• if the points on a scatter diagram follow a linear pattern.
• if the line of best fit is a straight line.

Question 5

What is a residual on a graph?

Answer 5

The vertical distance from the line of best fit to a point.

Question 6

What is the regression line of y on x?

Answer 6

The line that minimises the sum of the squares of the residuals (the least squares regression line).

(Where the residuals are a minimum)

Question 7

What is the equation of the regression line of y on x?

Answer 7

y = a + bx

Question 8

Are the coded regression line and actual regression line the same?

Answer 8

No, as the linear change may affect the answer.

Question 9

What is interpolation?

Answer 9

When you estimate the value of a dependent variable within the range of the data.

Question 10

What is extrapolation?

Answer 10

When you estimate a value outside the range of the data. Values estimated by extrapolation can be unreliable.

Question 11

Name one use of a regression line?

Answer 11

To estimate the value of the dependent variable for any value of the independent variable.