Bivariate Data, Correlations, R and R Squared

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

• r² > 0.5

• the correlation coefficient is positive

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

• y-intercept = −0.52 & slope = −1.2

• y-intercept = 0 & slope = −1.2

• y-intercept = 0.52 & slope = −1.2

• y-intercept = −1.2 & slope = 0.52

• y-intercept = 1.2 & 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:

• 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, s_x = 1.871 and s_y = 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 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 is closest to:

• y = 20 + 0.8x

• y = 0.8 + 2x

• y = 2 + 0.8x

• y = 1.2 + 2x

• y = 2 + 1.2x