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…

## 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…

## 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:…

## 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…

## 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…

## 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…

## 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…

## 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…

## 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…

## BTEC Level 3 Unit 1: Information Technology Systems – Strategy, Management and Infrastructure, Internal Set Assignment, UK

Unit in brief Learners study the role of computer systems and the implications of their use in personal and professional situations. Unit introduction Information technology (IT) systems play a significant role in the world around us. They play a key…