Question

A sample of n = 16 people is obtained, for each subject two variables are measured: hours slept in a typical night and clinical anxiety scores. the sample average anxiety score is 15 with a standard deviation of 3 the sample average hours slept is 7.5 with a standard deviation of 2 The correlation between anxiety and hours slept is -0.7 Bonus fact: The sums of squared deivations (SS) for sleep = 60. The SS for anxiety = 135

a. what is the equation for the regression line for predicting sleep from anxiety? [3points]

b.  what is the standard error of the estimate for the regression line for predicting sleep from anxiety?

Answer 1

a.

Let Sleep variable be denoted as y and anxiety variable be denoted as x.

Slope b1 = r * (Sy / Sx)

= -0.7 * 2 / 3

= -0.4667

Intercept = = 7.5 - (-0.4667) * 15 = 14.5005

The equation for the regression line for predicting sleep from anxiety is,

Sleep (y) = 14.5005 - 0.4667 Anxiety (x)

b.

Sums of squared deivations (SS) for sleep = 60

SSyy = 60

SS for anxiety = 135

SSxx = 135

SSxy = b1 SSxx = -0.4667 * 135 = -63.0045

Sum of Squared residuals, SSE = SSyy - SSxy^2 / SSxx  

= 60 - (-63.0045)^2 / 135

= 30.5958

standard error of the estimate for the regression line for predicting sleep from anxiety is,

Se =

= 1.478315