Regression making predictions

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Presentation transcript:

Regression making predictions

Correlation vs. Regression Corr. Reg. Association Prediction Two variables X (IV) & Y (DV) Both free to vary X fixed, Y free Single coefficient Predicted values, Residuals, Strength of model statistics

Correlation vs. Regression Corr. Reg. Descriptive Inferential Regression bridges the gap between descriptive and inferential statistics. It is related to correlation, but is also used to test hypotheses.

Conceptual Introduction Linear regression gives us an equation. The equation describes a line that is the “line of best fit.” It is the line that best describes the relationship between variables. Think about shooting an arrow through the scatterplot, so that the arrow passes as close to all the points as possible.

Conceptual Introduction The “line of best fit”, or the arrow that passes through the scatterplot closest to the points, shows us where our predicted Y values are for given values of X.

Conceptual Introduction The line is like taking a running mean, or the average of Y for each value of X, and then smoothing it out to make a straight line. In a sense, our best prediction of Y for a given value of X, is the mean of all the Y values that have the particular value of X in question.

Conceptual Introduction Remember from algebra, that we describe a line with this equation: Y = mx + b In statistics we say: where: Y = b0 + b1x1 + e b0 = Y intercept Ypred = b0 + b1 x1 b1 = Slope

Perceived Stress = 67.651 - 7.238(Perceived Control) + e Predicted Perceived Stress = 67.651 - 7.238(Perceived Control)