Stat 3rd test
Correlation analysis
determines the strength of the relationship between the dependent and independent variables.
The ________ and the __________ always have the same sign
slope of the regression line, and the coefficient of correlation, (b and r).
Given: Y^=7-.5X, Coefficient of Determination=.81 At what point does the equation cross the y-axis? What is the Coefficient of Correlation? Increasing the independent variable by 1 will result in what amount of increase or decrease to the dependent variable?
7 -.9 decrease of .5
Regression analysis
describes how one dependent variable and one or more independent variables are related, used for the purpose of prediction.
Regression model
describes how the dependent and independent variables are related.
Explained sum of squares
E(Y^-Ybar)^2.
Unexplained sum of squares
E(Yi-Y^)^2.
Total sum of squares
E(Yi-Ybar)^2.
Total variation
Explained+Unexplained variation.
Slope
amount Y' increases when X increases by 1, represents the change in Y per unit change in X.
Coefficient of Correlation
equal to the coefficient of determination but it can be negative or positive, has the same sign as the slope in simple linear regression, measures the strength of the linear relationship between two variables, and is the square root of the coefficient of determination.
Independent variable
goes on the x-axis, variable being used to estimate, and used to predict dependent variable, can be manipulated by the investigator, explanatory, and predictor.
Dependent variable
goes on the y-axis, variable being estimated, variable that is being predicted, and response variable in regression analysis.
Scatter Diagram
graphic tool to show the relationship between X and Y.
Inverse linear relationship
if B is negative, and if X increases and Y decreases.
Direct linear relationship
if B is positive, and if X increases and Y increases.
No linear relationship
if B=0, and if X increases and Y can increase or decrease.
Simple linear regression
if the coefficient of correlation is zero, the the regression line can go through the origin but it doesn't have to.
Correlation Coefficient
may range from -1.00 to +1.00, interval measurements are required to compute, is zero if there is no correlation between two variables.
Standard Error of estimate
measure of the variation around the regression line, is zero if all the points on the scatter diagram lie on the regression line.
Least squares
minimizes the term E(Y-Y^) to find a and b.
Larger values of r^2 mean that
observations are more closely grouped about the least square line.
Coefficient of Determination
percent of explained variation, usually labeled r^2, determined by SSR/SS total, tells us the proportion of the total variation that is explained, and ranges from 0 to +1.00, is 1 if all the points lie on the least squares regression line.
Least square method
provides the best approximation for the relationship between the independent and dependent variables, used to arrive at the "best fitting" straight line in regression analysis.
Regression where b=0 means
regression equation is parallel to the X-axis.
Regression where a=0 means
regression equation is parallel to the Y-axis.
Regression surface
relationship among several variables.
The Y intercept
represents the predicted value of Y when X=0.
Confidence interval
shows the range of values of Y^.
Testing for the existence of correlation is qual to
testing for the existence of the slope (b1).
A coefficient of correlation was computed to be -.70, this means
that as the X value increases, the Y value decreases.
Regression analysis involving two quantitative variables, we assume
that the variation around the regression line are the same for each X.
Correlation means
the degree of association between two variables.
Interpretation of the standard error of the estimate is equal to,
the interpretation of the standard deviation.
The width of the confidence interval estimate for the predicted value of Y is dependent on:
the sample size, the value of X for which the prediction is being made, and the standard error of the estimate.
Given: y^=a+bx a is? b is?
the y intercept and the slope of the regression line.
Multiple regression analysis
there can be several independent variables but only one dependent variable.
If correlation coefficient (r)=1.00 then,
there is no unexplained variation.
Regression equation
used to estimate the value of the dependent variable based on the independent variable.
Intercept
value when X=0.
