In developing a multiple linear regression model in excel. How do I find the x and Y inputs. How do I find a 95% confidence interval for the mean market value for houses that are 30 years old and have 1,800 sq ft, and 95% prediction interval for a house that is 30 years old with 1,800 sq ft
To develop a multiple linear regression model in Excel, you need the dataset that includes both the dependent variable (Y) and the independent variables (Xs).
Here are the steps to find the X and Y inputs for your multiple linear regression model:
1. Ensure that your dataset is organized, with each observation or data point as a single row, and the variables in separate columns.
2. Identify the dependent variable (Y), which is the variable you want to predict or explain. For example, in this case, it could be the market value of houses.
3. Identify the independent variables (Xs), which are the variables that influence the dependent variable. For example, in this case, the independent variables could be the age of the house (X1) and the square footage (X2).
Once you have identified the X and Y inputs, you can proceed to perform the regression analysis and obtain the regression equation, coefficients, and other statistics in Excel.
Finding the confidence intervals and prediction intervals for the mean market value and a specific house can be done using the regression results and the appropriate formulas.
To find a 95% confidence interval for the mean market value for houses that are 30 years old and have 1,800 sq ft:
1. Plug in the values of the independent variables (age = 30, sq ft = 1800) into the regression equation to estimate the mean market value for this combination of variables.
2. Calculate the standard error of the estimate, which measures the accuracy of the predicted mean value. This can be found in the regression output in Excel.
3. Use the t-distribution and the degrees of freedom associated with the regression model to find the critical value for a 95% confidence interval. The degrees of freedom can also be found in the regression output.
4. Calculate the margin of error by multiplying the critical value by the standard error. This gives you the range within which the true mean market value is likely to fall.
5. Finally, construct the confidence interval by taking the estimated mean market value and adding and subtracting the margin of error.
To find a 95% prediction interval for a house that is 30 years old with 1,800 sq ft:
1. Calculate the standard error of the prediction, which takes into account both the error in estimation and the variation based on individual predicted values. This can be found in the regression output.
2. Use the t-distribution and the degrees of freedom associated with the regression model to find the critical value for a 95% prediction interval.
3. Calculate the margin of error by multiplying the critical value by the standard error of the prediction.
4. Construct the prediction interval by taking the estimated market value (point estimate) and adding and subtracting the margin of error.
Remember, these steps may vary slightly depending on the specific version of Excel you are using and the analysis tool you choose within Excel. Use regression functions or add-ins available in your Excel version to perform the analysis and find the required intervals.