Analyzing Bivariate Data Unit Test

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Question
Use the least squares method to find the slope of the line of best fit for the data set below. Round to three decimal places.

x 67 28 26 47 86 32 15 70
y 46 34 33 38 46 37 35 44(1 point)
Responses

−0.202
negative 0.202

−4.430
negative 4.430

0.202
0.202

4.430

1 answer

To find the slope of the line of best fit using the least squares method, we first need to calculate the correlation coefficient.

Using the given data set:

x: 67 28 26 47 86 32 15 70
y: 46 34 33 38 46 37 35 44

Calculating the correlation coefficient gives us r = 0.808

The slope of the line of best fit is given by the formula:
slope = r * (Sy / Sx)
where Sy is the standard deviation of y and Sx is the standard deviation of x.

From the data:
Sy = 5.901
Sx = 24.514

So, the slope can be calculated as:
slope = 0.808 * (5.901 / 24.514)
slope = 0.194 approx.

Therefore, the correct answer is 0.194, which rounded to three decimal places, is 0.194.