Which of the following are assumptions made in the calculation of regression inferential statistics?

true
The errors of prediction are normally distributed.
false
X is normally distributed.
false
Y is normally distributed.
true
The variance around the regression line is the same for all values of X.
true
The relationship between X and Y is linear.
The assumptions are linearity, homoscedasticity, and normally distributed errors. See the text for more information.
The slope of a regression line is 0.8, and the standard error of the slope is 0.3. The sample used to compute this regression line consisted of 12 participants. Compute the 95% confidence interval for the slope. Type the upper limit of the confidence interval in the box below.

Use the table in this section or the inverse t distribution calculator to find that the critical value is t(N-2) = t(10) = 2.23. The upper limit of the 95% CI = b + (t)(sb) = .8 + 2.23(.3) = 1.47.
1.47
0.031
In a sample of 20, the correlation between two variables is .5. Determine if this correlation is significant at the .05 level by calculating the t value.

t = (r) sqrt(N-2)/sqrt(1-r^2) = (0.5) sqrt(18)/sqrt(1-.25) = 2.45 (This is significant at the .05 level.)
2.45
0.051
Calculate the lower limit of the 95% confidence interval for the correlation of .75 (N = 25).

First, convert r to z' (so .75 -> .973). The standard error of z' is 1/sqrt(N-3) = .213. Lower limit of CI = .973 - 1.96(.213) = 0.556. Now convert back from z' to r. r = .505
.505
0.006