Simple least squares regression problem. Am I doing anything wrongly?

• bobthebanana
In summary, the least squares regression of Y on A-D is based on a sample size of 506. The regression equation is Y = 11.08 - 0.954*A - 0.134*B + 0.255*C - 0.052*D and the R^2 value is 0.581. To test the null hypothesis that the coefficient on D is equal to 0, the normalcdf function is used and the result is 0, leading to the rejection of the null hypothesis. A 95% confidence interval for the coefficient on D is constructed as 0.052 +/- 1.96*0.006, and there is a 95% probability that this interval contains the true population

bobthebanana

Least squares regression of Y on A-D based on sample size of 506

Y = 11.08 - 0.954*A - 0.134*B + 0.255*C - 0.052*D
s.errs (0.32) (0.117) (0.043) (0.019) (0.006)

R^2 = 0.581

problem A. Test null that coefficient on D is equal to 0
d = coefficient on D
null: D ~ N(0, 0.006)
Pr(d >= 0.052) = 1 - normalcdf(0.052 / 0.006) = 0
reject

problem B. Construct 95% confidence interval for coefficient on D
0.052 +/- 1.96*(0.006 / sqrt(506))

problem C. What is the probability that this interval contains the true population regression coefficient on D?
? just 95%?

___________

The problem gives a lot of info and I only use very little of it, which leads me to believe I'm doing something wrongly. Am I?

Thanks for the help!

Looks okay except in part B. The output of the regression is giving you the estimated standard deviation of D, so you don't have to divide by sqrt(506). If you wanted to nitpick you could use the t distribution instead of the normal distribution, but since you have 506 observations it is probably not an issue.

What is a simple least squares regression problem?

A simple least squares regression problem is a statistical method used to model the relationship between two variables. It is used to find the best fitting line that minimizes the sum of squared residuals (the difference between the observed values and the values predicted by the regression line). This line can then be used to make predictions about future data points.

What are the assumptions of a simple least squares regression?

The main assumptions of a simple least squares regression are that the relationship between the two variables is linear, the residuals are normally distributed, the errors are independent, and the variances of the errors are equal. Violations of these assumptions can lead to inaccurate results and conclusions.

How do I interpret the results of a simple least squares regression?

The results of a simple least squares regression are typically presented in the form of a regression equation, with the coefficient (slope) and intercept values. The coefficient represents the change in the dependent variable for every unit increase in the independent variable. The intercept represents the predicted value of the dependent variable when the independent variable is equal to 0. Additionally, the p-value and R-squared value can provide information about the significance and strength of the relationship between the variables.

What is the purpose of performing a residual analysis in a simple least squares regression?

A residual analysis is used to assess the validity of the assumptions of a simple least squares regression. It involves plotting the residuals (the difference between the observed values and the values predicted by the regression line) against the predicted values. If the residuals show a random pattern with no clear trends, it indicates that the assumptions of the regression are met. However, if there are systematic patterns or trends in the residuals, it suggests that the model may need to be adjusted.

What can I do if my data violates the assumptions of a simple least squares regression?

If your data does not meet the assumptions of a simple least squares regression, there are a few options available. You can try transforming the data to make it more linear, using a different type of regression (such as a non-linear regression), or using robust regression methods that are more tolerant to violations of the assumptions. It is also important to carefully interpret the results and consider the potential limitations of the analysis.