# Linear regression predicts a response to a predicted

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skew the statistics. Linear regression predicts a response to a predicted value but the response may vary morethan expected. Errors can still be reduced. Linear regression reduces errors with optimal estimates. The variance in a variable is measured with the average squared deviation from its mean. In simple regression, the square of the correlation coefficient, r², is the fraction of the variance of the data values.Consider the correlation of the number of years of education and annual income level. In the scatterplot, a positive correlation was displayed with a correlation coefficient of 0.94. The regression equation can be calculated from the given information:
Mean of x=3Mean of x=29Standard deviation of x=2.1 Standard deviation of y=8.7 The slope of the regression equation is , and: The y-intercept of the regression equation is , and Thus, the regression equation is: Y’The correlation coefficient isr = 0.94, therefore the = 0.94² = 0.88.Using the regression equation, predictions can be made for any value for x. Consider the value of 5 for x. Y’In other words, the annual income level for five years of higher education is \$36,800.
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