![]() ![]() An alternative way to describe all four assumptions is that the errors, \(\epsilon_i\), are independent normal random variables with mean zero and constant variance, \(\sigma^2\). Connecting the dots - that is, the averages - you get a line, which we summarize by the formula \(\mu_Y=\mbox(\epsilon_i)\), at each value of the predictor, \(x_i\), is zero. And, similarly, take the average college entrance test score for students with a GPA of 2, 3, and 4. In both these cases, all of the original data points lie on a straight line.Now, take the average college entrance test score for students with a GPA of 1. If r = –1, there is perfect negativecorrelation. If r = 1, there is perfect positive correlation. If r = 0 there is absolutely no linear relationship between x and y (no linear correlation). Values of r close to –1 or to +1 indicate a stronger linear relationship between x and y. ![]() Estimate simple linear regression equations to identify which of the following has the strongest linear relationship with annual salary: the. The size of the correlation rindicates the strength of the linear relationship between x and y. The management of a technology company is trying to determine the variable that best explains the variation of employee salaries using a sample of 52 full-time employees see the file P1411.xlsx. What the VALUE of r tells us: The value of r is always between –1 and +1: –1 ≤ r ≤ 1. If you suspect a linear relationship between x and y, then r can measure how strong the linear relationship is. ![]() In real life we know that although the equation makes a. ![]() Use your calculator to find the least squares regression line and predict the maximum dive time for 110 feet. In practice, we make estimates of the parameters and substitute the estimates into the equation. The data in the table show different depths with the maximum dive times in minutes. SCUBA divers have maximum dive times they cannot exceed when going to different depths. ![]()
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