Question

The correlation coefficient r between the values assumed by two variables, X

Answer 1

The slope of the line of best fit to the raw-score scatter plot is 0.98

• The equation is y = 0.98x - 3.74
• The value of y given that x = 12 is 8.02

How to determine the slope of the line?

From the question, we have the following parameters that can be used in our computation:

• Standard deviations of X, Sx = 1.88
• Standard deviations of Y, Sy =2.45
• Correlation coefficient, r between X and Y = 0.75

The slope (b) of the line is calculated as

b = r * Sy/Sx

Substitute the known values in the above equation, so, we have the following representation

b = 0.75 * 2.45/1.88

Evaluate

b = 0.98

The equation of the line of best fit

A linear equation is represented as

y = bx + c

Where

Slope = b

y-intercept = c

In (a), we have

b = 0.98

So, we have

y = 0.98x + c

Recall that the point (13, 9) is on the line of best fit.

So, we have

9 = 0.98 * 13 + c

This gives

9 = 12.74 + c

Evaluate

c = -3.74

So, we have

y = 0.98x - 3.74

The value of y from x

Here, we have

x = 12

So, we have

y = 0.98 x 12 - 3.74

Evaluate

y = 8.02

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