For a given set of data, it is known that x = 10 and y = 4. The gradient of the regression line y on x is 0.6. Find
the equation of the regression line and use it to estimate y when x = 8.
To find the equation of the regression line, we need to use the given data point (x = 10, y = 4) and the gradient of the regression line (0.6).
The equation of a regression line is given by:
y = mx + c
where m is the gradient and c is the y-intercept.
Step 1: Find the y-intercept (c)
To find the y-intercept (c), we need to substitute the given data point (x = 10, y = 4) into the equation and solve for c.
4 = 0.6 * 10 + c
4 = 6 + c
c = 4 - 6
c = -2
So, the y-intercept (c) is -2.
Step 2: Substitute the values of m and c into the equation.
Substituting the values of the gradient (m = 0.6) and the y-intercept (c = -2) into the equation, we get:
y = 0.6x - 2
Therefore, the equation of the regression line is y = 0.6x - 2.
Step 3: Estimate y when x = 8.
To estimate the value of y when x = 8, we substitute x = 8 into the equation of the regression line:
y = 0.6 * 8 - 2
y = 4.8 - 2
y = 2.8
Therefore, the estimated value of y when x = 8 is 2.8.