Statistics- It can be fun (?) to take data and calculate regression equations

QUESTION

1. It can be fun (?) to take data and calculate regression equations, and many scholarly papers do this. But when we want to use that data to make predictions, that is for a given x value what y value do we predict, we don’t always use the regression equation we just calculated. If the value of | r | is high based on Table A-6 and if we are not forecasting for an x value too far from the sample data, use the regression model to predict the y value corresponding to the x value. But if these conditions don’t hold, then the best predicted value of y is the average of the y values, y bar. Here is an analogy of the above: Heights and IQs of adult males have no correlation, so if you were predicting the IQ of a 6 foot male, you would not substitute x = 6 feet into the regression equation and calculate y, but instead you would use the average IQ (average of the y values) which is about 100. But if you were predicting the time it would take to drive 125 miles, where r is high, you would mentally be doing a calculation of how long it takes to drive 55 miles, how long it takes to drive 110 miles, and so on, and you would be mentally estimating a regression equation for data whose r value is high. Does the above make sense? if it makes sense why do it make sense?2. Excel will calculate the correlation coefficient r for you:=CORREL(range of x values, range of y values) returns the correlation coefficient r. So will Statdisk. Enter the data in the first two columns of the editor with the x data in column 1 and the y data in column 2. Then ANALYSIS > CORRELATION & REGRESSION > EVALUATE gives you r. If you know r, then r * r = r2. If you know r2, =√(r2) gives you the absolute value of r, but doesn’t tell you if r is negative. Does it matter in calculating r, which dataset you call the x variable and which dataset you call the y variable? Do this example 2 from page 501. Confirm you get r=.591. Now reverse x and y, and report to the class with your conclusion.x29.729.731.431.827.6y175.3177.8185.4175.3172.7

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