10.2
The linear correlation coefficient R measures the strength of what in a sample?
The linear relationship between x and y values
What is regression equation?
y= a+ bX
y=Bo+BiX
How do you find coefficient of determination easily?
r^2
Perfect fit is and poor fit is .
R^2 = 1, R^2 = 0
R is between what two values?
-1 and 1
How do you get the regression equation from a calculator?
Stat- Calc - #4 Line Reg - plug values into regression equation
What is the equation (in words or in numbers) of total variation?
Total Variation = Explained Variation + Unexplained Variation
Or E(y - ybar)^2 = E(yhat - ybar)^2 + E(y - yhat)^2
What P-Value is the best predictor?
P-Value that is the lowest or closest to 0.
If R>CV and you reject the Null, what does this mean?
There is a significant linear correlation
How do you find the minimum sum in the Least Squares Property?
Square the vertical deviations from the regression line and add them together
Use the value of the linear coefficient r to find the coefficient of determination:
r = 0.333
.110889
Identify the adjusted value for R^2.
54.4% or .544
Is there or is there not a significant linear correlation? significance level= .05 n = 20 r = .203
CV> r Fail to reject Null; There is not significant evidence to assume that it is a linear correlation
Using a calculator, find the regression line of this data:
X: 0, 1, 1, 2, 5
Y: 3, 3, 4, 5, 6
y=.622x + 3.081
Find the coefficient of determination from the following data:
X: 1 2 3 5 6
Y: 5 8 11 17 20
(y = 2 + 3x)
.580
Identify the P-Value corresponding to the overall significance of the multiple regression equation.
0.116
What is the linear correlation coefficient of this data?
X: 43, 21, 25, 42, 57, 59
Y: 99, 65, 79, 75, 87, 70
r= .291
For the regression equation y=30.116x +4.047, find the value of x= .75. Test for significance first if you know that r = .645 and the CV = +/- .707.
It is significant and y= 14.37
Find the standard error of estimate for the following data:
X: -62 -41 -36 -26 -33 -56 -50 -66
Y: 21 13 12 3 6 22 14 19
(equation of regression line: y = -6.49522 -0.437735x)
2.790
Identify the multiple regression equation.
HHSIZE = .92 - .244METAL + 1.75PLASTIC - .073FOOD