Exponential Regression Newton’s Method – Advanced

Exponential Regression Newton’s Method – Advanced Property 1: Given samples {x1, …, xn} and {y1, …, yn} and let ŷ = αeβx, then the value of α and β that minimize (yi − ŷi)2 satisfy the following equations: Proof: The minimum is obtained when the first partial derivatives are 0. Let Thus we seek values for α and β such that  and ; i.e. Property 2: Under the same […]

Real Statistics Exponential Regression Capabilities

Real Statistics Exponential Regression Capabilities In Exponential Regression using a Linear Model we review Excel’s approach to exponential regression using linear regression. The Real Statistics Resource Pack provides a more accurate, nonlinear, exponential regression model. Real Statistics Functions: The following functions are provided in the Real Statistics Resource Pack. Here R1 contains a column range with the values for x and […]

Exponential Regression using Newton’s Method

Exponential Regression using Newton’s Method We now show how to create a nonlinear exponential regression model using Newton’s Method. Property 1: Given samples {x1, …, xn} and {y1, …, yn} and let ŷ = αeβx, then the value of α and β that minimize (yi − ŷi)2 satisfy the following equations: Proof: For a proof using calculus, click here Property 2: Under the same assumptions as Property […]

Exponential Regression using Solver

Exponential Regression using Solver The Excel model described in Exponential Regression using a Linear Model suffers from the shortcoming that it doesn’t actually minimize the sum of the squares of the deviations. We now show how to use Solver to create a better, nonlinear, regression model. Example 1: From the data for Example 1 of Exponential Regression using a […]

Confidence and prediction intervals for forecasted values

Confidence and prediction intervals for forecasted values Objective On this webpage, we explore the concepts of a confidence interval and prediction interval associated with simple linear regression, i.e. a linear regression with one independent variable x (and dependent variable y), based on sample data of the form (x1, y1), …, (xn, yn). We also show how to […]

Testing the significance of the slope of the regression line

Testing the significance of the slope of the regression line We now show how to test the value of the slope of the regression line. Basic Approach By Property 1 of One Sample Hypothesis Testing for Correlation, under certain conditions, the test statistic t has the property But by Property 1 of Method of Least Squares and by Definition […]

Fitness of Regression Line Test

Fit of the Regression Line Basic Concepts On this webpage, we show how to test the following null hypothesis: H0: the regression line doesn’t capture the relationship between the variables If we reject the null hypothesis it means that the line is a good fit for the data. We now express the null hypothesis in […]

Regression Analysis Using Excel

Regression Analysis The goal of regression analysis is to describe the relationship between two variables based on observed data and to predict the value of the dependent variable based on the value of the independent variable. Even though we can make such predictions, this doesn’t imply that we can claim any causal relationship between the […]

Method of Least Squares Using Excel

Method of Least Squares In Correlation we study the linear correlation between two random variables x and y. We now look at the line in the xy plane that best fits the data (x1, y1), …, (xn, yn). Recall that the equation for a straight line is y = bx + a, where b = the slope of the line a = y-intercept, i.e. […]

printer variations

SURVEYING FINAL ASSIGNMENT (This assignment is marked out of 80 but is worth 40% of the subject assessment)  Using the plan provided, and meeting the criteria set out below, you must make a preliminary design for a road to access a rural property. The new road must run from its junction with Tucker’s Road and […]