Can someone please help me on these I have look at the examples and done just what they did, but I still get it wrong and I only have one more time to try.

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 Incorrect: Your answer is incorrect.1.5 .
3 Incorrect: Your answer is incorrect.2.5 .
5 Incorrect: Your answer is incorrect.3.5 .
7 Incorrect: Your answer is incorrect.4.5 .
9 Incorrect: Your answer is incorrect.5.5 .

(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.-0.5 . 3 Incorrect: Your answer is incorrect.0.5 .
2 Incorrect: Your answer is incorrect. . 3
6 Incorrect: Your answer is incorrect. . 2 Incorrect: Your answer is incorrect. .
1 5
3 3

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

This is similar to a previous question.

I believe it would do you good to plot the scatter diagram and calculate the regression line according to the formula.
Post again if you have difficulties.
For your information, the regression coefficient a is between 0 and 0.2, the constant b is between 2 and 3.
The formula for se² has been given in the answer of your previous post.

To find the equation of the line of best fit, you can use the method of least squares.

Step 1: Calculate the means of x and y.

Mean of x (x̄) = (1 + 1 + 3 + 3 + 5 + 5 + 7 + 7 + 9 + 9) / 10 = 5
Mean of y (ȳ) = (3 + 2 + 6 + 1 + 3 + 3 + 3 + 2 + 5 + 3) / 10 = 3.1

Step 2: Calculate the differences between each x and its mean, and each y and its mean.

x - x̄: -4, -4, -2, -2, 0, 0, 2, 2, 4, 4
y - ȳ: -0.1, -1.1, 2.9, -2.1, -0.1, -0.1, -0.1, -1.1, 1.9, -0.1

Step 3: Calculate the sum of the products of these differences.

Sum of (x - x̄)(y - ȳ): 98

Step 4: Calculate the sum of the squares of the differences of x from its mean.

Sum of (x - x̄)^2: 80

Step 5: Calculate the equation of the line of best fit.

The equation of the line of best fit is given by:
y hat = ȳ + (Sum of (x - x̄)(y - ȳ)) / (Sum of (x - x̄)^2) * (x - x̄)

Substituting the values:
y hat = 3.1 + 98 / 80 * (x - 5)

So, the equation of the line of best fit is y hat = -0.775x + 6.725.

To find the ordinates y hat for the points on the line of best fit whose abscissas are x = 1, 3, 5, 7, and 9, you can plug these values into the equation of the line of best fit.

For x = 1:
y hat = -0.775 * 1 + 6.725 = 5.95

For x = 3:
y hat = -0.775 * 3 + 6.725 = 4.625

For x = 5:
y hat = -0.775 * 5 + 6.725 = 3.3

For x = 7:
y hat = -0.775 * 7 + 6.725 = 1.975

For x = 9:
y hat = -0.775 * 9 + 6.725 = 0.65

So, the ordinates y hat for the points on the line of best fit are:
1: 5.95
3: 4.625
5: 3.3
7: 1.975
9: 0.65

To find the value of e for each of the points above (e = y - y hat), you can subtract the y hat values from the corresponding y values.

For y = 3:
e = 3 - 5.95 = -2.95

For y = 2:
e = 2 - 4.625 = -2.625

For y = 6:
e = 6 - 3.3 = 2.7

For y = 1:
e = 1 - 1.975 = -0.975

For y = 3:
e = 3 - 0.65 = 2.35

So, the values of e for each of the points are:
-2.95, -2.625, 2.7, -0.975, 2.35

To find the variance se^2 of those points about the line of best fit, you can calculate the sum of the squares of these residuals and divide it by the number of points minus 2.

Step 1: Calculate the squared residuals.

Squared residuals:
(-2.95)^2 = 8.7025
(-2.625)^2 = 6.890625
(2.7)^2 = 7.29
(-0.975)^2 = 0.950625
(2.35)^2 = 5.5225

Step 2: Calculate the sum of the squared residuals.

Sum of squared residuals = 8.7025 + 6.890625 + 7.29 + 0.950625 + 5.5225 = 29.35675

Step 3: Divide the sum of squared residuals by the number of points minus 2.

Number of points = 5
Variance se^2 = Sum of squared residuals / (Number of points - 2) = 29.35675 / 3 = 9.78558333

So, the variance se^2 of those points about the line of best fit is 9.78558333.