Use the following table to answer the questions. (Give your answers correct to two decimal places.)

x 1 1 3 3 5 5 7 7 9 9
y 3 2 6 1 3 3 3 2 5 3

(a) Find the equation of the line of best fit.
y hat = + x

(ii) Graph this equation on a scatter diagram. (Do this on paper. Your instructor may ask you to turn in this work.)

(b) Find the ordinates y hat for the points on the line of best fit whose abscissas are x = 1, 3, 5, 7, and 9.
1
3
5
7
9

(c) Find the value of e for each of the points above (e = y - y hat).
y e y e
3 Incorrect: Your answer is incorrect. . 3
2 Incorrect: Your answer is incorrect. . 3
6 2
1 5
3 3

(d) Find the variance se2 of those points about the line of best fit.

I do not want you to work them out, I just need help on formulas the ones in the book I do not understand so I was hoping there is a easier formula out there that someone might no of.

To find the equation of the line of best fit, we can use linear regression.

(a) Find the equation of the line of best fit:
Step 1: Calculate the mean values for x and y.
Mean of x: (1 + 1 + 3 + 3 + 5 + 5 + 7 + 7 + 9 + 9) / 10 = 5
Mean of y: (3 + 2 + 6 + 1 + 3 + 3 + 3 + 2 + 5 + 3) / 10 = 3.1

Step 2: Calculate the slope of the line (m):
m = Σ((x - mean of x) * (y - mean of y)) / Σ((x - mean of x)^2)
= ((1-5)*(3-3.1) + (1-5)*(2-3.1) + (3-5)*(6-3.1) + ... + (9-5)*(5-3.1)) / ((1-5)^2 + (1-5)^2 + (3-5)^2 + ... + (9-5)^2)

Step 3: Calculate the intercept (b):
b = mean of y - (m * mean of x)

Using these steps, calculate the equation of the line of best fit.

(ii) Graph this equation on a scatter diagram:
Plot the given points (x, y) on a graph and then plot the line of best fit using the equation you found in part (a).

(b) Find the y-hat values for the given x values:
Substitute each x value (1, 3, 5, 7, 9) into the equation of the line of best fit to find the corresponding y-hat values.

(c) Find the value of e for each of the points:
Calculate the residual (e) for each point by subtracting the predicted y-hat value from the actual y value.

(d) Find the variance se^2 of those points about the line of best fit:
Calculate the sum of squared residuals (Σ(e^2)) and divide it by the degrees of freedom (n-2) to find the variance.

Remember to round your answers to two decimal places as instructed.