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