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

See similar textbooks

Similar questions

A property agent wants to study the relationship between the age of a house (X) and its selling price (Y). Listed below is a random sample of houses that the agent has sold recently. [House] [Age in Years (X)] [Selling Price in $'m (Y)] 1 9 2.2 2 7 1.9 3 11 1.7 4 12 0.8 5 8 2.5 a) Determine the linear regression equation. b) i. If the age of a house is 10 year-old, what is the selling price? ii. If the age of a house is 20 year-old, what is the selling price? c) i. Determine the correlation coefficient. ii. Interpret the result.
Consider the following data: - 4 - 3 - 1 P(X = x) 0.2 0.1 0.2 0.1 0.4 Step 4 of 5: Find the value of P(X > -2). Round your answer to one decimal place.
3. The relationship between variables Y (RM billion), X (%) and Z (million tons) can be illustrated by the following linear regression model. Yi = Bot BiXit BeZit Hi A summary of the data for the three variables from year 1988 to 2018 is as follows: Σκ. = 192.734 Σy² = 55,541.86 [vix = 403.937 Sy = 4.304 Where y₁=Y₁ - Y x₁ = X₁ - X Z₁ = Z₁ - Z (a) Use the Ordinary Least Squares Method (OLS) to estimate all the parameters in the model. Ex= [x² = 3.029 = 1.899 Yi Zi Στις Ez = 535.562 = 5,112.319 Σχ Sz = 0.423 Sx = 0.032 = 39.522 XZ₁ = 39.492 (b) Use the standardized regression coefficients to compare the effect of X and Z on Y respectively. (c) Calculate the elasticity of Y with respect to Z at the mean value. Explain the meaning of the elasticity value obtained.
8
6- For one of the simple linear regression model Σ(iyi) = 150 and ² = 50. Find slope coefficiem B₁. (Please be careful x and y are lower letters) 10 3 8 5 0,33 18032
Consider the following data for two variables, x and y. \ table[[x, 9, 32, 18, 15, 26], [y, 9, 19, 20, 16, 22]] (a) Develop an estimated regression equation for the data of the form hat(y) = b + b₁x. (Round bo to two decimal 1 0 places and b₁ to three decimal places.) hat 1 (y) = 8.65 +0.427x Comment on the adequacy of this equation for predicting y. (Use α = 0.05.) The high p- value and low coefficient of determination indicate that the equation is inadequate. The high p-value and high coefficient of determination indicate that the equation is adequate. The low p-value and low coefficient of determination indicate that the equation is inadequate. The low p-value and high coefficient of determination indicate that the equation is adequate. hat 2 (y) = 10.54 +2.618x-0.054x Comment on the adequacy of this equation for predicting y. (Use a =0.05.) The high p-value and low coefficient of determination indicate that the equation is inadequate. The high p-value and high coefficient of…
The authors of the paper "Power-Load Prediction Based on Multiple Linear Regression Model"t were interested in predicting the load on the electric power system in China using data on y = Power consumption (in hundreds of millions of kwh), x, Population (in millions), and x, = Gross domestic %3D product (in billions of dollars), for 21 years. The model equation proposed in the paper is y = -113,527 + 0.974x, + 0.057x, + e. (a) According to this model, what is the mean power consumption (in hundreds of millions of kwh) for a year if the population was 160,000 million and the gross domestic product was 600,000 billion dollars? hundreds of millions of kwh (b) Interpret the value of B, in this model. When the [ gross domestic product v is fixed, the mean increase in [power consumption (in hundreds of millions of kwh) V associated with a 1-million unit increase in [population is 0.974.
Step 1: The equation of the least-squares regression line for predicting dates' heights from women's heights for the data below is predicted height of date 41.08 0.42 x woman's height Heights of women (x) 66 64 63 65 70 65 72 68 70 68 71 64 Heights of their dates (y) (Fill in the blanks below and give your answers to 2 decimal places.) The slope is m = _(1) (2) inch on average. For each additional inch of women's height, the height of the next person dated goes up by eBook Answer 1 Answer 2
Suppose there is 1 dependent variable (dissolved oxygen, Y) and 3 independent variables (water temp X1, depth X2, and hardness of water X3). Below is the result of the multiple linear regression.Which of the following is the equation of the multiple regression model? Y = 4.36 + 0.37X1 + 0.24X2 + 0.04X3 Y = 0.00 + 0.02X1 + 0.56X2 + 0.37X3 Y = 24.84 - 1.17X1 - 0.15X2 - 0.04X3 Y = 5.69 – 3.20X1 - 0.61X2 -0.95X3
Calculate the estimate of σε What is the estimated resting heart rate for someone who is a smoker (Smoke=1) and exercises 1 hour a day (Exercise=1)?
Suppose that in a certain chemical process the reaction time y (hr) is related to the temperature (°F) in the chamber in which the reaction takes place according to the simple linear regression model with equation y = 5.10 0.01x and a = 0.085. USE SALT (a) What is the expected change in reaction time for a 1°F increase in temperature? For a 9°F increase in temperature? 1°F increase hr hr 9°F increase (b) What is the expected reaction time when temperature is 220°F? When temperature is 260°F? 220°F hr ✓hr 260°F 2.5 (c) Suppose five observations are made independently on reaction time, each one for a temperature of 260°F. What is the probability that all five times are between 2.37 and 2.63 hours? (Round your answer to four decimal places.) (d) What is the probability that two independently observed reaction times for temperatures 1° apart are such that the time at the higher temperature exceeds the time at the lower temperature? (Round your answer to four decimal places.) 0.4602 X You…
The below data on the production volume x and total cost y (in dollars) for a particular manufacturing operation were used to develop the estimated regression equation y = 1,217.33 + 7.68x. Production Volume Total Cost ($) $ (units) 400 Submit Answer 450 550 600 700 750 4,100 4,900 5,400 5,900 6,500 (a) The company's production schedule shows that 650 units must be produced next month. What is the point estimate of the total cost (in dollars) for next month? (Round your answer to the nearest cent.) $6209.33 7,000 (b) Develop a 99% prediction interval for the total cost (in dollars) for next month. (Round your answers to the nearest cent.) X to $ X (c) If an accounting cost report at the end of next month shows that the actual production cost during the month was $6,700, should managers be concerned about incurring such a high total cost for the month? Discuss. Since $6,700 is within the prediction interval, managers should not be concerned about Incurring such a high total cost for one…

SEE MORE QUESTIONS

Recommended textbooks for you

MATLAB: An Introduction with Applications

Statistics

ISBN:

9781119256830

Author:

Amos Gilat

Publisher:

John Wiley & Sons Inc

Probability and Statistics for Engineering and th…

Statistics

ISBN:

9781305251809

Author:

Jay L. Devore

Publisher:

Cengage Learning

Statistics for The Behavioral Sciences (MindTap C…

Statistics

ISBN:

9781305504912

Author:

Frederick J Gravetter, Larry B. Wallnau

Publisher:

Cengage Learning

MATLAB: An Introduction with Applications

Statistics

ISBN:

9781119256830

Author:

Amos Gilat

Publisher:

John Wiley & Sons Inc

Probability and Statistics for Engineering and th…

Statistics

ISBN:

9781305251809

Author:

Jay L. Devore

Publisher:

Cengage Learning

Statistics for The Behavioral Sciences (MindTap C…

Statistics

ISBN:

9781305504912

Author:

Frederick J Gravetter, Larry B. Wallnau

Publisher:

Cengage Learning

Elementary Statistics: Picturing the World (7th E…

Statistics

ISBN:

9780134683416

Author:

Ron Larson, Betsy Farber

Publisher:

PEARSON

The Basic Practice of Statistics

Statistics

ISBN:

9781319042578

Author:

David S. Moore, William I. Notz, Michael A. Fligner

Publisher:

W. H. Freeman

Introduction to the Practice of Statistics

Statistics

ISBN:

9781319013387

Author:

David S. Moore, George P. McCabe, Bruce A. Craig

Publisher:

W. H. Freeman

SEE MORE TEXTBOOKS