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Calculate linear regression equation4/15/2024 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. This equation itself is the same one used to find a line in algebra but remember, in statistics the points don’t lie perfectly on a line the line is a model around which the data lie if a strong linear. And, similarly, take the average college entrance test score for students with a gpa of 2, 3, and 4. The formula for the best-fitting line (or regression line) is y mx + b, where m is the slope of the line and b is the y -intercept. Now, take the average college entrance test score for students with a gpa of 1. And, similarly, the data on the entire subpopulation of students with gpas of 2, 3, and 4 are plotted. That is, the data on the entire subpopulation of students with a gpa of 1 are plotted. As you can see, there are so many data points - each representing one student - that the data points run together. Let's focus for now just on those students who have a gpa of 1. Below is a plot illustrating a potential relationship between the predictor "high school grade point average (gpa)" and the response "college entrance test score." Only four groups ("subpopulations") of students are considered - those with a gpa of 1, those with a gpa of 2. Let's investigate this question with another example. But, we haven't yet discussed what b 0 and b 1 estimate. We have worked hard to come up with formulas for the intercept b 0 and the slope b 1of the least squares regression line.
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