Question

In a simple linear regression analysis, the following data represents the relationship between x and y: x: 5, 10, 15, 20, 25 y: 12, 18, 24, 30, 36 Calculate the equation of the regression line y on x:

a. x=1.2y+6
b. y=1.2x+6
c. x=1.5y+8
d. y=1.5x+8

Answer 1

The equation of the regression line is y = 1.2x + 6.

The equation of a simple linear regression line is given by: y = mx + b

where m is the slope of the line and b is the y-intercept.

The equation of the regression line, you need to calculate the slope and y-intercept.

The slope can be calculated using the formula:

m = (n(∑xy) - (∑x)(∑y)) / (n(∑
`x^2`) - (∑(x)^2) and

the y-intercept can be calculated using the formula:

b = (∑y - m(∑x)) / n.

Let's calculate the slope and y-intercept using the given data:

• n = 5
• ∑x = 75
• ∑y = 120
• ∑xy = 1800
• ∑
  `x^2` = 1875

After performing the calculations, the slope (m) is found to be 1.2 and the y-intercept (b) is 6.

Therefore, the equation of the regression line is: y = 1.2x + 6. The correct answer is b. y = 1.2x + 6.

Answer 2

The equation of the regression line for the provided data is y = 1.2x + 6, which can be determined by calculating the slope and y-intercept from the given points.

Step-by-step explanation:

To calculate the equation of the regression line for the given data, we need to find the slope (b) and the y-intercept (a) of the line using the formula y = a + bx, where x is the independent variable and y is the dependent variable. Since the data given is perfectly linear (as the increase in x by 5 results in an increase in y by 6 each time), we can calculate the slope (b) by taking any two points. For example, using the points (5, 12) and (10, 18), the slope b = (18 - 12) / (10 - 5) = 6 / 5 = 1.2. To find the y-intercept (a), we can substitute the slope b and one of the points into the equation. Using the point (5, 12), we get 12 = a + 1.2(5), giving a = 12 - 6 = 6. Therefore, the equation of the regression line is y = 1.2x + 6.