Question

Some statistical methods require that the residuals from a regression line have a normal distribution. Consider the following residuals.

0.37	-0.70	0.10	-0.34	0.19	0.61	-0.26	-0.98
1.64	-0.18	-0.23	0.54	-0.54	-1.11	0.93	-0.03

(b) Find the regression line of mean score on time step-by-step. First calculate the mean and standard deviation of each variable and their correlation (use a calculator with these functions). Then find the equation of the least-squares line from these. (Round your answers to two decimal places.)
? =  +  x

Draw the line on your scatterplot. What percent of the year-to-year variation in scores is explained by the linear trend? (Round your answer to one decimal place.)
%

Answer 1

Descriptive Statistics: x, y

Variable Mean StDev
x -0.126 0.543
y 0.127 0.872

Correlation: x, y

Pearson correlation of x and y = -0.102

Regression Analysis: y versus x

Model Summary

S R-sq R-sq(adj) R-sq(pred)
0.937266 1.04% 0.00% 0.00%

Coefficients

Term Coef SE Coef T-Value P-Value  
Constant 0.107 0.341 0.31 0.765
x -0.164 0.653 -0.25 0.811  

Regression Equation

y = 0.107 - 0.164 x

1.04 percent of the year-to-year variation in scores is explained by the linear trend .