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We expect that students who do well on the midterm exam in a course will usually do well on the final exam. Gary smith of pomona college looked at the exam scores of all 346 students who took his statistics class over a 10-year period. Assume that both the midterm and final exam were scored out of 100 points. State the equation of the least-squares regression line if each student scored the same on the midterm and the final.

Respuesta :

If each student scored the same on the midterm and final, the equation of the least-squares regression line is [tex]\hat{y}=x[/tex].

What are equations?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.

For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

So, Gary Smith of Pomona College reviewed the test results of all 346 students who took his statistics course over a ten-year period.

Take into account that both the midterm and final tests were rated out of 100.

Let the midterm score (x) and the final score (y) be the same.

The data for the explanatory variable x and the response variable y will be the same if each student receives the same grade on the midterm and final.

The linear model will predict that the two variables are equal if the data for the two variables are the same, and as a result, the linear model will assume that the expected y-variable is equal to the predicted x-variable.

Thus, the following is how the least-square regression line appears:

[tex]\hat{y}=x[/tex]

Therefore, if each student scored the same on the midterm and final, the equation of the least-squares regression line is [tex]\hat{y}=x[/tex].

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