l The Amount of Scatter in the data The multiple standard error of the estimate (-)2 n-k-1 where 1; =each observed value of y in the data set i,=the value of y that would have been estimated from the regression equation n= the number of data values in the set k=the number of independent(a) variables measures the dispersion of the data points around the regression hyperplane o 2002 The Wadsworth Group
The Amount of Scatter in the Data • The multiple standard error of the estimate where yi = each observed value of y in the data set = the value of y that would have been estimated from the regression equation n = the number of data values in the set k = the number of independent (x) variables measures the dispersion of the data points around the regression hyperplane. s e = (y i –y ˆ i )2 n–k–1 y ? i © 2002 The Wadsworth Group
I Approximating a Confidence Interval for a Mean of y a reasonable estimate for interval bounds on the conditional mean of y given various x values is generated by 予士 where the estimated value of y based on the set of x values provided t= critical t value,(1-a)% confidence, df=n-k-1 s, the multiple standard error of the estimate o 2002 The Wadsworth Group
Approximating a Confidence Interval for a Mean of y • A reasonable estimate for interval bounds on the conditional mean of y given various x values is generated by: where = the estimated value of y based on the set of x values provided t = critical t value, (1–a)% confidence, df = n – k – 1 se = the multiple standard error of the estimate n e s y ˆ ±t× y ? © 2002 The Wadsworth Group