Next highlight the array of observed values for y (array R1), enter a comma and highlight the array of observed values for x (array R2) followed by a right parenthesis. To use TREND(R1, R2), highlight the range where you want to store the predicted values of y. TREND(R1, R2, R3) = array function which predicts the y values corresponding to the x values in R3 based on the regression line based on the x values stored in array R2 and y values stored in array R1. TREND(R1, R2) = array function which produces an array of predicted y values corresponding to x values stored in array R2, based on the regression line calculated from x values stored in array R2 and y values stored in array R1. Thus FORECAST(x, R1, R2) = a + b * x where a = INTERCEPT(R1, R2) and b = SLOPE(R1, R2). INTERCEPT(R1, R2) = y-intercept of the regression line as described aboveįORECAST( x, R1, R2) calculates the predicted value y for the given value of x. SLOPE(R1, R2) = slope of the regression line as described above Here R1 = the array of y data values and R2 = the array of x data values: Thus a and b can be calculated in Excel as follows where R1 = the array of y values and R2 = the array of x values:ī = SLOPE(R1, R2) = COVAR(R1, R2) / VARP(R2)Ī = INTERCEPT(R1, R2) = AVERAGE(R1) – b * AVERAGE(R2)Įxcel Functions: Excel provides the following functions for forecasting the value of y for any x based on the regression line.
Since the terms involving n cancel out, this can be viewed as either the population covariance and variance or the sample covariance and variance. Observation: The theorem shows that the regression line passes through the point ( x̄, ȳ) and has the equation Two proofs are given, one of which does not use calculus.ĭefinition 1: The best fit line is called the regression line. Theorem 1: The best fit line for the points ( x 1, y 1), …, ( x n, y n) is given byĬlick here for the proof of Theorem 1. A mathematically useful approach is therefore to find the line with the property that the sum of the following squares is minimum. The best fit line is the line for which the sum of the distances between each of the n data points and the line is as small as possible. the value of y where the line intersects with the y-axisįor our purposes, we write the equation of the best fit line asįor each i, we define ŷ i as the y-value of x i on this line, and so Recall that the equation for a straight line is y = bx + a, whereĪ = y-intercept, i.e. We now look at the line in the xy plane that best fits the data ( x 1, y 1), …, ( x n, y n). In Correlation we study the linear correlation between two random variables x and y.
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