Question

A regression line has a slope of 1.885 if the mean of the x-coordinates of the data points is 3448 and the means of the y-coordinates is 12.312 what is the y-itercept of the line to three decimal places

Answer 1

The y-intercept of the line is -6487.168

How to get the y-intercept?

Sure, I can help with that. The y-intercept of the regression line can be found using the following formula:

y-intercept = mean of y-coordinates - slope * mean of x-coordinates

In this case, we have:

• Slope = 1.885
• Mean of x-coordinates = 3448
• Mean of y-coordinates = 12.312

Plugging these values into the formula, we get:

y-intercept = 12.312 - 1.885 * 3448

y-intercept = -6487.168

Answer 2

The value of the slope c is -6,487.168

Explanation:

In this question, we are told to find the y-intercept of a regression line model.

Mathematically, a regression model having a single dependent variable y and a single independent variable x can be represented by the equation of a straight line.

This is the same as;

y = mx + c

where m is the slope and c is the y intercept

Now from the question, we know we are to calculate c , where y is the mean of the y-coordinates at a value of 12.312, where x is also the mean of the x-coordinates at a value of 3448 and an m-value which is the slope at 1.885

We plug these values into the straight line equation to yield;

12.312 = 1.885(3448) + c

c = 12.312 - 1.885(3448)

c = 12.312 - 6,499.48

c = -6,487.168