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
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Introduction to Linear Regression and Correlation Analysis Goals After this‚ you should be able to: • • • • • Calculate and interpret the simple correlation between two variables Determine whether the correlation is significant Calculate and interpret the simple linear regression equation for a set of data Understand the assumptions behind regression analysis Determine whether a regression model is significant Goals (continued) After this‚ you should be able to: • Calculate and
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THE BASIS OF STATISTICAL TESTING * samples and populations * population – everyone in a specified target group rather than a specific region * sample – a selection of individuals from the population * sampling * simple random sampling – identify all the people in the target population and then randomly select the number that you need for your research * extremely difficult‚ time-consuming‚ expensive * cluster sampling – identify clustering
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Linear Regression & Best Line Analysis Linear regression is used to make predictions about a single value. Linear regression involves discovering the equation for a line that most nearly fits the given data. That linear equation is then used to predict values for the data. A popular method of using the Linear Regression is to construct Linear Regression Channel lines. Developed by Gilbert Raff‚ the channel is constructed by plotting two parallel‚ middle lines above and below a Linear Regression
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Problems on Regression and Correlation Prepared by: Dr. Elias Dabeet Q1. Dr. Green (a pediatrician) wanted to test if there is a correlation between the number of meals consumed by a child per day (X) and the child weight (Y). Included you will find a table containing the information on 5 of the children. Use the table to answer the following: Child Number of meals consumed per day (X) child weight (Y) X² Y² XY Ahmad 11 8 121 64 88 Ali 16 11 256 121 176 Osama 12 9 144
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LINEAR REGRESSION MODELS W4315 HOMEWORK 2 ANSWERS February 15‚ 2010 Instructor: Frank Wood 1. (20 points) In the file ”problem1.txt”(accessible on professor’s website)‚ there are 500 pairs of data‚ where the first column is X and the second column is Y. The regression model is Y = β0 + β1 X + a. Draw 20 pairs of data randomly from this population of size 500. Use MATLAB to run a regression model specified as above and keep record of the estimations of both β0 and β1 . Do this 200 times. Thus you
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1. Calculate real GDP for 2004 and 2005 using 2004 prices. To calculate the real GDP we use the constant price for 2004 which was $20. Real GDP (base year 2004) 2004 ($20 per CD x 100 CD’s) + ($110 per racquet x 200 racquets) = 24000 2005 ($20 per CD x 120 CD’s) + ($110 per racquet x 210 racquets) = 25500 By what percentage did real GDP grow? Because the Real GDP was $24000 in 2004 and $25500 in 2005‚ real GDP grew by ($25500 - $24000) / $24000 = 0.0625 or 6.25% 2. Calculate the
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Exercise 27 5. In the legend beneath Figure 2[->0]‚ the authors give an equation indicating that systolic blood pressure is SBP = 43.2 + 0.17x. If the value of x is postnatal age of 30 hours‚ what is the value for Ŷ or SBP for neonates ≤1‚000 grams? Show your calculations. Y = a + bx 43.2 + 0.17(30) = 48.3 The SBP for neonates ≤1‚000 grams at 30 hours is 48.3. 6. In the legend beneath Figure 2[->1]‚ the authors give an equation indicating that systolic blood pressure is SBP = 50.3 + 0.12x
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Answers to Midterm Test No. 1 1. Consider a regression model of relating Y (the dependent variable) to X (the independent variable) Yi = (0 + (1Xi+ (i where (i is the stochastic or error term. Suppose that the estimated regression equation is stated as Yi = (0 + (1Xi and ei is the residual error term. A. What is ei and define it precisely. Explain how it is related to (i. ei is the residual error term in the sample regression function and is defined as eI hat = Y
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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
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