Chapter 4 Simple regression model Practice problems

Use Chapter 4 Powerpoint question 4.1 to answer the following questions: 1. Report the Eveiw output for regression model .
Please write down your fitted regression model.

2. Are the sign for consistent with your expectation, explain?

3. Hypothesize the sign of the coefficient and test your hypothesis at 5% significance level using t-table.

4. What percentage of variation in 30 year fixed mortgage rate is explained by this model? Why?

Use Chapter 4 Powerpoint question 4.2 to answer the following questions:

5. Report the Eveiw output for regression model
Based on the estimation period of 1986.01 – 1999.07. Please write down your fitted regression model.

6. Is Trend correlated with USPI? Set up the hypothesis testing at 5% significance level.

7. What percentage of variation in USPI is explained by this model? Why?

8. Based on your Eview model, report your forecast of USPI for the period of 1999.08-2000.07. Report RMSE.

Use Chapter 4 Powerpoint question 4.3 to answer the following questions:

9. Report the Eveiw output for regression model USPIt = (USTBR)t + t based on the estimation period of 1986.01 – 1999.07. Please write down your fitted regression model.

...The simpleregressionmodel (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). SimpleRegressionModel (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...

...
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 estimated regression equation and explain what the slope of the line indicates. d. Compute the coefficient of determination and comment on the strength of relationship between x and y. e. Compute the sample correlation coefficient between the price and the number of flash drives sold. f. Perform a t test and determine if the price and the number of flash drives sold are related. Let α = 0.01. g. Perform an F test and determine if the price and the number of flash drives sold are related. Let α = 0.01. |
ANS:
b. Negative linear relationship.
c. | = 29.7857 - 0.7286xThe slope indicates that as the price goes up by $1, the number of units sold goes down by 0.7286 units. |
d. | r 2 = .8556; 85.56% of the variability in y is explained by the linear relationship between x and y. |
e. | rxy = -0.92; negative strong relationship. |
f. t = -5.44 < -4.032 (df = 5); reject Ho, and conclude x and y are related.
g. | F = 29.642 > 16.26; reject Ho, x...

...This article considers the relationship between two variables in two ways: (1) by using regression analysis and (2) by computing the correlation coefficient. By using the regressionmodel, we can evaluate the magnitude of change in one variable due to a certain change in another variable. For example, an economist can estimate the amount of change in food expenditure due to a certain change in the income of a household by using theregressionmodel. A sociologist may want to estimate the increase in the crime rate due to a particular increase in the unemployment rate. Besides answering these questions, a regressionmodel also helps predict the value of one variable for a given value of another variable. For example, by using the regression line, we can predict the (approximate) food expenditure of a household with a given income. The correlation coefficient, on the other hand, simply tells us how strongly two variables are related. It does not provide any information about the size of the change in one variable as a result of a certain change in the other variable.
Let us return to the example of an economist investigating the relationship between food expenditure and income. What factors or variables does a household consider when deciding how much money it should spend on food every week or every month? Certainly, income of the household is one factor....

...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 y-intercept of 10 and a slope of 4, then when x = 2 the actual value of y is:
a. 18
b. 15
c. 14
d. unknown
ANSWER: d
3. Given the least squares regression line [pic]= 5 –2x:
a. the relationship between x and y is positive
b. the relationship between x and y is negative
c. as x increases, so does y
d. as x decreases, so does y
ANSWER: b
4. A regression analysis between weight (y in pounds) and height (x in inches) resulted in the following least squares line: [pic]= 120 + 5x. This implies that if the height is increased by 1 inch, the weight, on average, is expected to:
a. increase by 1 pound
b. decrease by 1 pound
c. increase by 5 pounds
d. increase by 24 pounds
ANSWER: c
5. A regression analysis between sales (in $1000) and advertising (in $100) resulted in the following least squares line: [pic] = 75 +6x. This implies that if advertising is $800, then the predicted...

...-------------------------------------------------
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 tendency toward the average height of all men. Today, the word “Regression” is used in quiet different sense. Its investigation depends upon two variables. Dependent and Independent Variable.
Definition
“Regression provides an equation to be used for estimating the average value of the dependent variable from the known values of independent variable.”
Determination and Probabilistic Relation or Model
The relation among variable may or may not be governed by an exact physical law. For convenience, let us consider a set of n pairs of observations (Xi , Yi). If the relation between the variables is exactly linear, then the mathematical equation describing the linear relation is generally written as
Yi = a + bXi
Where a is the value of Y when X equals zero and is called Y-intercept and b indicates the change in Y for a one-unit change in X and is called the slope of the line. Substituting a value for X in the equation, we can completely...

...EXECUTIVE SUMMARY
The study is undertaken to study retailers behavior towards Aircel in selected region. The data is collected directly by visiting outlets through structured interview scheduled. The statistical tools used to analyze the data are: Co-relation analysis, Simple Linear Regression and Multiple Linear Regression. The software used to analyze the data is Windostat version 8.6, developed by Indostat services, is an advanced level statistical software for research and experimental data analysis.
The study is carried mainly in the areas like Lokthkunta, Lalbazar, Kharkhana, Old Alwal, Suraram, Medchal, Miyapur, Balanagar, Bollaram, Yapral, Anandbagh, Malkajgiri, ECIL areas in Hyderabad city.
1. INTRODUCTION
Telecommunication was one of the world powerful tool of development. It is one of the key changer for continuous growth and in areas of reducing poverty, employment development, gender equity, balanced regional development and special protection for vulnerable sections of the society. Indian telecommunication sector has undergone as a growth engine for the Indian economy in the last decade with the country experiencing huge growth in wireless sector. The penetration of internet and broadband has also improved.
Telecom sector is broadly divided into:
1. Fixed line telephony.
2. Mobile telephony.
a. Global System for Mobile Communications (GSM) and
b. Code Division Multiple Access (CDMA)....

...will perform a regression analysis to determine the effect of the Unemployment Rate (UR) on Total New Houses Sold (TNHS). I expect that there will be a negative relationship between the two variables. In other words, as the unemployment rate increases, the total number of new houses sold will decrease.
The simple functional form of the model is TNHS=f(UR), where TNHS (measured in thousands) is the dependent variable and UR (16 years and over) is the explanatory variable. To determine the relationship between the two variables, one must set up the Population Regression Function (PRF). The PRF represents the regression line of the population as a whole. The deterministic PRF for the model is E(TNHSt|UR) = B₁ + B₂URt. B1 and B2 are population parameters. B₁ is the intercept coefficient and represents TNHS when UR is zero. In regression analysis, the population regression function is estimated on the basis of the sample regression function (SRF). That is, the PRF is an estimator of the SRF. The deterministic SRF in this case is TNHS = b1 + b2UR. In this function, b1 and b2 are estimators for B1 and B2 in the PRF. The PRF and SRF functions in their stochastic forms are:
PRF: TNHSt = B1 + B2URt + Ut
SRF TNHSt = b1 + b2URt + et
In the PRF, Ut is the population error term. The population error term is a random variable that cannot be explained by...

...STATISTICS FOR MGT DECISIONS
FINAL EXAMINATION
Forecasting – Simple Linear Regression Applications
Interpretation and Use of Computer Output (Results)
NAME
SECTION A – REGRESSION ANALYSIS AND FORECASTING
1) The management of an international hotel chain is in the process of evaluating the possible sites for a new unit on a beach resort. As part of the analysis, the management is interested in evaluating the relationship between the distance of a hotel from the beach and the hotel’s average occupancy rate for the season. A sample of 14 existing hotels in the area is chosen, and each hotel reports its average occupancy rate. The management records the hotel’s distance (in miles) from the beach. The following set of data is obtained:
Distance (miles) 0.1 0.1 0.2 0.3 0.4 0.4 0.5 0.6 0.7
Occupancy (%) 92 95 96 90 89 96 90 83 85
Continue
Distance (miles) 0.7 0.8 0.8 0.9 0.9
Occupancy (%) 80 78 76 72 75
Use the computer output to respond to the following questions:
a) A simple linear regression was ran with the occupancy rate as the dependent (explained) variable and distance from the beach as the independent (explaining) variable
Occpnc = b[pic] + b[pic](Distncy)
What is the estimated regression equation?
The regressionmodel is: Occpnc = b[pic] + b[pic](Distncy)
The estimated regression equation...

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