ITM- Chapter 13- Simple Linear Regression
Coefficient of Determination
measures the proportion of variation in Y that is explained by the independent variable X in the regression model
Standard Error of the Estimate
measures the variability of the actual Y values from the predicted Y values in the same way as standard deviation
Least squares method
minimizes the sum of the squared differences between the actual values (yi) and the predicted Y values
Four Assumption of Regression
Linearity, Independence of Errors, normality of Error, and Equal Variance
Simple Linear Regression
a single numerical independent variable, X, is used to predict the numerical dependent variable Y, such as using the size of a store to predict the annual sales of the store.
Regression Analysis
enables you to develop a model to predict the values of a numerical variable, based on the value of other variables
Predicted Value of Y
equals the Y intercept plus the slope multiplied by the value of X.
Slope
expected change in Y per unit change in X
Relevant range
includes all the values from the smallest to the largest X used in developing the regression model
The residual or estimated error value
is the difference between the observed Yi values and the predicted values of the dependent variable for a given value of Xi.
Total Sum of Squares (SST)
is the measure of variation of the Yi values around their mean, Ybar.
random error
is the vertical distance of the actual value Yi above or below the expected value.
Regression Sum of Squares (SSR)
represents that variation that is explained by the relationship between X and Y,
Error Sum of Squares
represents the variation due to factors other than the relationship between X and Y.
Independence of Errors
requires that the errors are independent of one another
Normality
requires that the errors are normally distributed at each value of X.
Equal Variance
requires that the variance of the errors be constant for all values of X.
Regression Coefficients
sample Y intercept and sample slope
Linearity
states that the relationship between the variables is linear
Y intercept
the mean value of Y when X equals 0.
The larger the Coefficient of Determination
the stronger the linear relationship between the independent and dependent variable
Dependent Variable
the variable you wish to predict
Independent Variable
the variables used to make the prediction