Question

In: Statistics and Probability

what is the least squares model and what statistical support do you have that this model...

what is the least squares model and what statistical support do you have that this model has any value?

Solutions

Expert Solution

Least Square Model:

The least squares method is a form of mathematical regression analysis that finds the line of best fit for a dataset, providing a visual demonstration of the relationship between the data points. Each point of data is representative of the relationship between a known independent variable and an unknown dependent variable.

In otherwords, A mathematical procedure for finding the best-fitting curve to a given set of points by minimizing the sum of the squares of the offsets ("the residuals") of the points from the curve. The sum of the squares of the offsets is used instead of the offset absolute values because this allows the residuals to be treated as a continuous differentiable quantity. However, because squares of the offsets are used, outlying points can have a disproportionate effect on the fit, a property which may or may not be desirable depending on the problem at hand.

A linear regression line has an equation of the form Y = a + bX, where X is the explanatory variable and Y is the dependent variable. The slope of the line is b, and a is the intercept (the value of y when x = 0).

We have a straight line(regression equation) that we can use to predict values of Y from values of X, which is one of the main uses of regression.


Related Solutions

What are Least Squares Assumptions for simple linear regression? For each least squares assumption, provide an...
What are Least Squares Assumptions for simple linear regression? For each least squares assumption, provide an example in which the assumption is valid, then provide an example in which the assumption fails.
Do you have a favorite statistical method? Is there a statistical method that you think you...
Do you have a favorite statistical method? Is there a statistical method that you think you will/already use in your workplace? v
what is linear least-squares approximation. could you show an example
what is linear least-squares approximation. could you show an example
The purpose of subjecting your BSA protein standard plot data to the least squares statistical method...
The purpose of subjecting your BSA protein standard plot data to the least squares statistical method was to a. determine intuitively the best fit straight line. b. statistically determine the best straight line through a series of experimental points. c. determine the overall shape of the BSA standard curve. d. determine the protein concentration in the unknown samples.
what is the regression technique of ordinary least squares?
what is the regression technique of ordinary least squares?
1)If a linear model is correct, then a least squares fit is unbiased. Knowing that, why...
1)If a linear model is correct, then a least squares fit is unbiased. Knowing that, why would one want to use some form of penalized regression 2) Define the AIC criterion for logistic regression 3) continued) In the context of logistic regression, describe forward stepwise selection based on the AIC criterion.
Prove that the least squares estimates in a simple linear regression model are unbiased. Be sure...
Prove that the least squares estimates in a simple linear regression model are unbiased. Be sure to state carefully the assumptions under which your proof holds.
QUESTION 17 The process of creating a linear model of bivariate data. a. Least Squares Regression...
QUESTION 17 The process of creating a linear model of bivariate data. a. Least Squares Regression b. Variability c. Extrapolation d. Residual analysis QUESTION 18 The "Portion of Variability" is also known as the a. Correlation coefficient b. Regression line c. Fitted Value d. Coefficient of determination QUESTION 19 Linear regression models may not always acccurately reflect the pattern of data from which they are made a. TRUE b. FALSE QUESTION 20 The following data relates the time a student...
Use the least squares method to fit a simple linear model that relates the salary (dependent...
Use the least squares method to fit a simple linear model that relates the salary (dependent variable) to education (independent variable). a- What is your model? State the hypothesis that is to be tested, the decision rule, the test statistic, and your decision, using a level of significance of 5%. b – What percentage of the variation in salary has been explained by the regression? c – Provide a 95% confidence interval estimate for the true slope value. d -...
Use the normal equations to directly apply the least squares method (that is, do not use...
Use the normal equations to directly apply the least squares method (that is, do not use a transformation or Excel’s built in trendline function) to the given data for the indicated model. Compute D and dmax as bounds for cmax; what do these bounds suggest about improving the fit by using the Chebyshev criterion? x 1 2 3 4 5 y 1 1 2 2 4 a. y = ax + b b. y = ax2 Analyze the deviations for...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT