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The simple linear regression equation keyboard

There is no meaningful interpretation for the correlation coefficient as there is for the \(R^2\) value. Know what various correlation coefficient values mean.Know how to calculate the correlation coefficient r from the \(R^2\) value.Understand the cautions necessary in using the \(R^2\) value as a way of assessing the strength of the linear association.

Know how to interpret the \(R^2\) value.That is, they can be 0 even if there is a perfect nonlinear association. Know that the coefficient of determination (\(R^2\)) and the correlation coefficient (r) are measures of linear association.Interpret the intercept \(b_\) from Minitab's fitted line plot and regression analysis output.Understand the concept of the least squares criterion.Distinguish between a deterministic relationship and a statistical relationship.The relationship between the dependent variable and each independent variable should be linear and all observations should be independent.Upon completion of this lesson, you should be able to: The variance of the distribution of the dependent variable should be constant for all values of the independent variable. Other assumptions: For each value of the independent variable, the distribution of the dependent variable must be normal.Categorical variables, such as religion, major field of study or region of residence, need to be recoded to binary (dummy) variables or other types of contrast variables. Data: Dependent and independent variables should be quantitative.

Plots: Consider scatterplots, partial plots, histograms and normal probability plots.

Also, consider 95-percent-confidence intervals for each regression coefficient, variance-covariance matrix, variance inflation factor, tolerance, Durbin-Watson test, distance measures (Mahalanobis, Cook and leverage values), DfBeta, DfFit, prediction intervals and case-wise diagnostic information. BearsReg Example - Regression Model, Residual Analysis Find the simple linear regression equation for predicting weight from height for the 1985 Chicago.

For each model: Consider regression coefficients, correlation matrix, part and partial correlations, multiple R, R2, adjusted R2, change in R2, standard error of the estimate, analysis-of-variance table, predicted values and residuals.

For each variable: Consider the number of valid cases, mean and standard deviation.

Assumptions to be considered for success with linear-regression analysis: