3. Consider a simple linear regression model (Y: Consumption, X: Disposable Income)Y = Bi + B2Xiteaccording to the data (n = 10) given, we haveY =nΣ(x − x)2-i=1Σi=1nΣΥ; - 1)2i=1ΣXiYii=1ei = 1.2X = 3 ΣX=30 Σx = 147i=1= 57n7 Y₁ = 70 Y² = 597= 107=1i=1ni=1ni=1n225, (X-X)(Y₂ - Y) = 15i=1(a) Obtain the estimates of 32 and 3₁ based on the numerical information given above.(b) Calculate the estimate of Var (3₂).(4)(c) Write down your fitted regression (estimated regression) model, and interpret the results.(d) Predict Yo value (the level of consumption) when the value of Xo (Income level) is givenby 12.

The given model is as follows:The given values are as follows:n =10,

Answered: 3. Consider a simple linear regression…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Suppose you estimate a regression equation Income = α + β1Experience + β2Business + β3Gender + β4Private + β5Experience*Gender + ε Income - annual income is in thousands of dollars (1 unit of income = $1000);Experience is in years;Business is a dummy variable set to 1 if person has a business degree, 0 otherwise;Gender is a dummy variable set to 1 for females, 0 for males;Private is a dummy variable set to 1 if a person attended private college, 0 otherwise; The data are on individuals who graduated from college within last 10 years. 1.) A. Use information from Question 1 . What is the average income of males with non-business degree, who went to public college, and who have 3 years of experience? (to 3 decimal points) B. Use information from Question 1 What is the average income of females with non-business degree, who went to public college, and who have 6 years of experience? (to 3 decimal points) C. Use information from Question 1. Which of the following statements is a correct…
4. Write a Julia function to calculate CV and GCV in the case of smoothing by local linear regression.
41. Which of the following is the multiple regression model for the data? (a) y = -0.11050 + 2.10797x1 + 0.40717x2 (b) y = -0.11050 + 0.40717x1 + 2.10797x2 (c) y = 0.23563 + 0.00062x1 + 0.23626x2 (d) none (e) y = -0.44187 + 2.42120x1 + 0.36135x2
Is the price elasticity of demand for cars statistically significant at 10% significant level? Explain.
3
Some non-linear regressions can also be estimated using a linear regression model (using 'linearization'). Assume that the data below show the selling prices y (in dollars) of a certain equipment against its age x (in years). We'd like to fit a non-linear regression in the form y = cd* to estimate parameters c and d from the data by linearizing the model through In y In c+ (In d)x = b, + b, x. y y 6381 3 5394 5673 4980 2 5740 4896 (Click the button to copy or download the data.) Using Excel ot other software, the non-linear regression model y = cd can be estimated as: y = D*. (Round c and d to four decimal places, inlcuding any zeros.)
the following regression table where the dependent variable is the demandfor massage services in one city in the United States. Specifically, the dependent variable is the number of customers per hour (Models 1 and 2) or per day (Models 3 and 4). a) Explain why the coefficient for Population/1,000 in Model 2 is very different from the one in Model 4?
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1. Simple Linear Regression Estimation: (а) For the model y; B1 + B2x; + ui, define the fitted value ĝ; and residual û;. (b) x to arrive at estimates for B1 and B2? How does OLS take data on the outcome variable y and the independent variable Suppose you have the OLS estimate of the slope coefficient B2 from regressing ax; is equal to (c) y on x. Show that the slope coefficient if you regressed y on x* for x B2/a, where a is some constant. To be clear, I want you to show that B = B2/a, where B2 is the OLS estimate of B2 from the model Yi = B1 + B2x; + ui, and B is the OLS estimate of B; from the model y; = Bi + B5x + U;.
Town A B C D E F GPopulation (lakh) (X ) 11 14 14 17 17 21 25No. of TV sets demanded ('000) (Y ) 15 27 27 30 34 38 46Fit a linear regression of Y on X and estimate the demand for TV sets for a city with apopulation of (a) 20 lakh and (b) 32 lakh.
Q10. price based on two features. Suppose we are going to apply multivariate Linear Regression to predict the house x1 = age of the house (0 – 40) x2 = quality of neighbouring schools (0 – 3) h(8) = 0, + 8,x1 + 02x2 Suggest one way to scale the features. Describe what will happen if feature scaling is not performed before the training process is conducted.
Tristan has completed his STAT 1342 course. He intends to build a simple linear regression model using control variable (X) as number of hours per week for his preparations and (Y) as the weekly performance measured in a 100-point scale and based on his self-assessment. There were totally n = 28 weekly collected records. The model built by Tristan was: Ý = 10 + 7· X with the standard error of estimated slope equal to SE = SE [6] = 2.8 1. At the significance level, a = 0.01, is there sufficient evidence that X positively impacts Y? • Evaluate Test Statistic • Specify critical value (or values) for this procedure • State the Rejection Rule • Formulate your decision 2. Estimate the population slope (= B) with confidence level, C = 0.95 • Specify critical value (or values) for this procedure • Evaluate UCL and LCL Solution 10

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