Question

Students at a number of universities were asked if they agreed that their education was worth the cost. One variable in the table is the percentage of students at the university who responded strongly agree. The other variable in the table is the ranking of the university reported by a national publication.

Ranking Percentage
of Alumni Who
Strongly Agree
28 53
29 57
30 62
37 56
45 54
47 63
52 55
54 63
57 70
60 59
65 66
66 56
72 65
75 58
82 67
88 60
98 75

Find the equation of the least squares line would allow you to predict the percentage of alumni who would strongly agree that their education was worth the cost, using ranking as the independent variable. (Round your answers to three decimal places.)

Answer 1

To find the least squares regression line predicting the percentage of alumni who strongly agree their education was worth the cost based on university ranking, you would use statistical software with the given data points and round the intercept and slope coefficients to three decimal places.

Step-by-step explanation:

You are asking how to find the equation of the least squares line to predict the percentage of alumni who would strongly agree that their education was worth the cost, using university ranking as the independent variable.

To find this equation, we need to apply the method of least squares, which minimizes the sum of the squares of the residuals (the differences between observed and predicted values).

Generally, the equation of a least squares line has the form ŷ = a + bx where:

• 'a' is the y-intercept of the line.
• 'b' is the slope of the line.
• 'x' represents the values of the independent variable.
• 'ŷ' represents the predicted values of the dependent variable.

However, without the actual data points, I cannot calculate the specific values of 'a' and 'b'. You would usually use statistical software or a calculator to input all the data (values for ranking and percentage of alumni who strongly agree) and then calculate the least squares regression line.

The coefficients 'a' and 'b' would be rounded to three decimal places as you requested, yielding a final equation of the form ŷ = a + bx.