Let's break down your queries step by step.

1. Error Calculation and Regression Line

Given the dataLet's break down your queries step by step.

1. Error Calculation and Regression Line

Given the

X	Y	Ŷ
2	1	3
4	4	4
7	5	6
9	7	10
10	11	8
13	12	9

Error is calculated as $\text{Error} = Y - \hat{Y}$.

Absolute Error is calculated as $|\text{Error}|$.

Now, let's compute these values:

X	Y	Ŷ	Error (Y - Ŷ)	Absolute Error
2	1	3	-2	2
4	4	4	0	0
7	5	6	-1	1
9	7	10	-3	3
10	11	8	3	3
13	12	9	3	3

2. Regression Equation

For the second dataset:

X	Y
1	2
2	4
3	6
12	240

You can calculate the regression coefficients using the formulas for linear regression. The formula for the regression line is $Y = a + bX$.

Let's calculate $b$ (slope) and $a$ (intercept):

1. Calculate the means of X and Y.
2. Use the formula for slope $b = \frac{N(\sum XY) - (\sum X)(\sum Y)}{N(\sum X^2) - (\sum X)^2}$.
3. Calculate $a$ using $a = \bar{Y} - b\bar{X}$.

The calculations will yield the regression equation.

3. Coefficients and Significance

For the regression table you provided:

Coefficientsa
Model	Unstandardized Coefficients
	B
(Constant)	3.919
X1	2.491
X2	-0.466

• The significance of coefficients can be checked using the p-values (Sig). Typically, a p-value < 0.05 indicates significance.
• The regression equation can be written as: $Y = 3.919 + 2.491X1 - 0.466X2$

Summary of Results:

1. Error and Absolute Error:

   • Error calculated for each data point.
   • Absolute error calculated as well.

2. Regression Equation:

   • Find slope and intercept for the second dataset.

3. Coefficients and Significance:

   • Constant and coefficients from the regression output.
   • Check significance using p-values.

If you need detailed calculations or explanations for any step, feel free to ask!

Questions for Further Exploration:

1. How do you interpret the slope and intercept of a regression line?
2. What methods can be used to evaluate the goodness of fit for a regression model?
3. How can multicollinearity affect the interpretation of regression coefficients?
4. What are potential reasons for a high error in regression predictions?
5. How can you visualize the regression line and errors graphically?

Tip:

Always check for outliers in your data, as they can significantly affect regression results and errors.