The simple regression model (SRM) is model for association in the population between an explanatory variable X and response Y. The SRM states that these averages align on a line with intercept β0 and slope β1: µy|x = E(Y|X = x) = β0 + β1x Deviation from the Mean

The deviation of observed responses around the conditional means µy|x are called errors (ε). The error’s equation: ε = y - µy|x Errors can be positive or negative, depending on whether data lie above (positive) or below the conditional means (negative).Because the errors are not observed, the SRM makes three assumptions about them: * Independent. The error for one observation is independent of the error for any other observation. * Equal variance. All errors have the same variance, Var(ε) = σε2. * Normal. The errors are normally distributed.

If these assumptions hold, then the collection of all possible errors forms a normal population with mean 0 and variance σε2, abbreviated ε ̴̴ N (0, σε2). Simple Regression Model (SRM) observed values of the response Y are linearly related to values of the explanatory variable X by the equation: y = β0 + β1x + ε, ε ̴̴ N (0, σε2) The observations:

1. are independent of one another,
2. have equal variance σε2 around the regression line, and 3. are normally distributed around the regression line.
21.2 Conditions for the SRM ( Simple Regression Model )
Instead of checking for random residual variation, we have three specific conditions. Checklist for the simple regression model * Is the association between y and x linear?
* Have we ruled out obvious lurking variables?
Errors appears to be a sample from a normal population.|
* Are the errors evidently independent?
* Are the variances of the residuals similar?
* Are the residuals nearly normal?
21.3 INTERFERENCE IN REGRESSION
Confidence intervals and hypothesis tests work as in inferences for the mean of a population: * The 95% confidence intervals for...

...Chapter 4 Simpleregressionmodel Practice problems
Use Chapter 4 Powerpoint question 4.1 to answer the following questions:
1. Report the Eveiw output for regressionmodel .
Please write down your fitted regressionmodel.
2. Are the sign for consistent with your expectation, explain?
3. Hypothesize the sign of the coefficient and test your hypothesis at 5% significance...

...
Simple Linear RegressionModel
1. The following data represent the number of flash drives sold per day at a local computer shop and their prices.
| Price (x) | Units Sold (y) |
| $34 | 3 |
| 36 | 4 |
| 32 | 6 |
| 35 | 5 |
| 30 | 9 |
| 38 | 2 |
| 40 | 1 |
| a. Develop as scatter diagram for these data. b. What does the scatter diagram indicate about the relationship between the two variables? c. Develop the...

...47
Review: Inference for Regression
Example: Real Estate, Tampa Palms, Florida Goal: Predict sale price of residential property based on the appraised value of the property Data: sale price and total appraised value of 92 residential properties in Tampa Palms, Florida
1000 900 Sale Price (in Thousands of Dollars) 800 700 600 500 400 300 200 100 0 0 100 200 300 400 500 600 700 800 900 1000 Appraised Value (in Thousands of Dollars)
Review: Inference for...

...Regression Analysis: A Complete Example
This section works out an example that includes all the topics we have discussed so far in this chapter.
A complete example of regression analysis.
PhotoDisc, Inc./Getty Images
A random sample of eight drivers insured with a company and having similar auto insurance policies was selected. The following table lists their driving experiences (in years) and monthly auto insurance premiums.
Driving Experience (years) Monthly...

...CHAPTER 16
SIMPLE LINEAR REGRESSION
AND CORRELATION
SECTIONS 1 - 2
MULTIPLE CHOICE QUESTIONS
In the following multiple-choice questions, please circle the correct answer.
1. The regression line [pic] = 3 + 2x has been fitted to the data points (4, 8), (2, 5), and (1, 2). The sum of the squared residuals will be:
a. 7
b. 15
c. 8
d. 22
ANSWER: d
2. If an estimated regression line has a...

...-------------------------------------------------
Simpleregression and correlation
Submitted by Sohaib Roomi
Submitted to:Miss Tahreem
Roll No M12BBA014
SimpleRegression
And Correlation
Introduction
The term regression was introduced by the English biometrician, Sir Francis Galton (1822-1911) to describe a phenomenon in which he observed in analyzing the heights of children and their parents. He solved a...

...1.
Qeach brand t=β0+β1*PMinute Maid t+β2*PTropicana t+β3*PPrivate label t+ueach brand t
Q: quantity P: price
By running the above regressionmodel for each brand, we got the following elasticity matrix and the figures for “V” and “C.” Note that we used the average price and quantity for P and Q to calculate each brand’s elasticity.
Price Elasticity | Tropicana | Minute Maid | Private Label |
Tropicana | -3.4620441 | 0.40596537 | 0.392997566 |
Minute Maid...

...de schattingen van de parameters beïnvloeden, het wordt dan onduidelijk of deze parameters zuiver zijn.
2.2 Monte Carlosimulatie
Om te onderzoeken in hoeverre autocorrelatie invloed heeft op het lineaire regressiemodel wordt er een model gecreëerd. Dit model bevat een onafhankelijke variabele (X) en een afhankelijke variabele (Y), het Monte Carlosimulatiemodel wordt hierop toegepast (Dougherty, 2002, p.72).
Met Monte Carlosimulatie als toepassing wordt als...