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
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.