Regression analysis

When using a least squares regression line to model a relationship displayed in a scatterplot, one key assumption is that

• there are two variables

• the variables are related

• the variables are linearly related

• the correlation coefficient is positive

In the least squares regression line y = -1.2 + 0.52x

• the y intercept = -0.52 and the slope = -1.2

• the y intercept = 0 and the slope = -1.2

• the y intercept = 0.52 and the slope = -1.2

• the y intercept = -1.2 and the slope = 0.52

• the y intercept = 1.2 and the slope = -0.52

If the equation of a least squares regression line is y=8-9x and R² = 0.25

• r = -0.5

• r = -0.25

• r = -0.0625

• r = 0.25

• r = 0.50

The least squares regression line y=8-9x predicts that when x=5, the value of y is:

• -45

• -37

• 37

• 45

• 53

A least squares regression line of the form y = a + bx is fitted to the data set shown. The equation of the line is:

• y=-0.69+24.4x

• y=24.4-0.69x

• y=24.4+0.69x

• y=28.7-x

• y=28.7+x

A least squares regression line of the form y = a + bx is fitted to the data set shown. The equation of the line is:

(HINT: Enter the x column first)

• y=1 + 0.5x

• y=0.5 + x

• y=0.5 + 7.5x

• y=7.5 + 0.5x

• y=30 - 0.5x

Given that r = 0.733, sx = 1.871 and sy = 3.391, the slope of the least squares regression line is closest to:

• 0.41

• 0.45

• 1.33

• 1.87

• 2.49

Using a least squares regression line, the predicted value of a data point is 78.6. The residual value is –5.4. The actual data value is:

• 73.2

• 84.0

• 88.6

• 94.6

• 424.4

The equation of the least squares regression line plotted on the scatterplot opposite is closest to:

• y = 8.7 − 0.9x

• y = 8.7 + 0.9x

• y = 0.9 − 8.7x

• y = 0.9 + 8.7x

• y = 8.7 − 0.1x

The equation of the least squares regression line plotted on the scatterplot opposite is closest to:

• y = −14 + 0.8x

• y = 0.8 + 14x

• y = 2.1 + 0.8x

• y = 14 - 0.8x

• y = 17 + 1.2x