I need help with the following questions Calculate the standard errors for a and b (sa and sb). Discuss the interpretation of each of them. Compute the confidence interval (alpha = 0.05) and the t-statistic for b. Again, explain the meaning of each of them in a sentence. Calculate the R2 for the regression and describe its meaning.
I need help with the following questions
- Calculate the standard errors for a and b (sa and sb). Discuss the interpretation of each of them.
- Compute the confidence interval (alpha = 0.05) and the t-statistic for b. Again, explain the meaning of each of them in a sentence.
- Calculate the R2 for the regression and describe its meaning.
- Graph the data points and the sample regression
function . Identify the slope and the intercept term. Label the data points and graphically indicate the residual for each observation. Add a vertical dashed line for the mean of X and the horizontal dashed line for the mean of Y. Does the regression function pass through the intersection of these two lines?
This information should be used for you to solve
The calculations below should be done by applying the bivariate regression formulas. In other words, do them “by hand” using a calculator or in Excel in a manner that I can clearly see the formulas you have used. You should also check your calculations by entering the data into an Excel sheet and using the
- Show how to calculate a and b. In a sentence, discuss the interpretation of each of them.
- The linear regression line is Y = a+ bx
where a is the y intercept and b is the slope
The value of b is calculated using the formula,
The value of a is calculated using the mean of x, mean of y and the slope as
Thus, the regression equation of Y on X is, Y = 10.24 - 0.524x
The y intercept value is 10.24 and the slope is -0.524. Since the slope is negative, the y increases as x decreases.
- Calculate the predicted value of Y and the residual for each observation.
The predicted value is calculated as
For, x = 17, Y = 10.24 - (0.524*17) = 1.332
For, X = 13, Y = 10.24 - (0.524*13) = 3.428
For X = 8, Y = 10.24 - (0.524*8) = 6.048
For, X = 10, Y = 10.24 - (0.524*10) = 5
For, X = 2, Y = 10.24 - (0.524*2) = 9.192
The residual value is calculated as follows:
|
S.No |
X |
Y |
|||
|
1 |
17 |
1 |
1.332 |
-0.332 |
0.110 |
|
2 |
13 |
3 |
3.428 |
-0.428 |
0.183 |
|
3 |
8 |
5 |
6.048 |
-1.048 |
1.098 |
|
4 |
10 |
7 |
5 |
2 |
4 |
|
5 |
2 |
9 |
9.192 |
-0.192 |
0.037 |
|
Sum |
50 |
25 |
|
|
5.428 |
- Calculate the Sum of Square Errors (SSE), Mean Square Error (MSE) and the Standard Error (s). Explain the meaning of each of them.
From the table, the error sum of square is 5.428. Since,
The mean error sum square is calculated using the SSE as
The standard error for slope is calculated by
Thus,
The standard error of intercept is calculated as
Standard error is helps to accurate the mean of the sample from the population likely to compare with the true population mean. As the standard error increase, there is more spread in the data set. Hence we remove the variable that cause the variation to get the better fit model.
Mean sum of square explains, how closely the variable to the regression line and we have to minimize this mean so that we get the best line that passes all through the point
Standard error of slope and intercept explains how closely the values are to the regression line. Form our value of slope standard error we say, they are closely related to the regression line, since our value is smaller.
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