2. Consider annual per-capita sales in tobacco (Y) and aggregate tobacco related advertisements (X) in the U.S. (the data are in millions of dollars). The sample size is n = 49. Tobacco Sales (Y) and Advertisement (X) The OLS results follows: a. 400 600 Advertisement (X) We are interested in estimating the relationship between advertisements and sales in tobacco: Y₁ =B₁ + B₂X₁ +u, b. Tobacco Sales (Y) C. d. 5000 4000 3000 2000 1000 0 0 Intercept Tobbaco Ad 200 Sum of Squares Mean Square Regression 13069027.5359 13069027.5359 Residual 27830633.2396 592141.1328 Total 40899660.7755 OLS Estimate Standard Error 2487.5635 2.6582 155.0608 0.5658 800 1000 By hand present an accurate plot of the fitted regression line, properly labeled (intercept, slope, etc.). Predict the value of tobacco sales based on advertisement outlays equal to 900. Consider the classical hypothesis: H₁: B₁ = 0 0 H₁: B₂ = 0 H₁: B₁ * 0 H₁: B₂ #0 Perform t-tests of the above hypotheses at the 10%, 5% and 1% levels. Comment on their outcomes, and the implications for our model of tobacco sales. Derive the R², compute the percent of the variance of Y captured by X, and comment on how well the model fits. Derive 95% CI's for the intercept and slope parameters. Comment on their sizes and how they relate to the test statistics computed above.
2. Consider annual per-capita sales in tobacco (Y) and aggregate tobacco related advertisements (X) in the U.S. (the data are in millions of dollars). The sample size is n = 49. Tobacco Sales (Y) and Advertisement (X) The OLS results follows: a. 400 600 Advertisement (X) We are interested in estimating the relationship between advertisements and sales in tobacco: Y₁ =B₁ + B₂X₁ +u, b. Tobacco Sales (Y) C. d. 5000 4000 3000 2000 1000 0 0 Intercept Tobbaco Ad 200 Sum of Squares Mean Square Regression 13069027.5359 13069027.5359 Residual 27830633.2396 592141.1328 Total 40899660.7755 OLS Estimate Standard Error 2487.5635 2.6582 155.0608 0.5658 800 1000 By hand present an accurate plot of the fitted regression line, properly labeled (intercept, slope, etc.). Predict the value of tobacco sales based on advertisement outlays equal to 900. Consider the classical hypothesis: H₁: B₁ = 0 0 H₁: B₂ = 0 H₁: B₁ * 0 H₁: B₂ #0 Perform t-tests of the above hypotheses at the 10%, 5% and 1% levels. Comment on their outcomes, and the implications for our model of tobacco sales. Derive the R², compute the percent of the variance of Y captured by X, and comment on how well the model fits. Derive 95% CI's for the intercept and slope parameters. Comment on their sizes and how they relate to the test statistics computed above.
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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Transcribed Image Text:2.
Consider annual per-capita sales in tobacco (Y) and aggregate tobacco related advertisements (X) in the U.S. (the
data are in millions of dollars). The sample size is n = 49.
Tobacco Sales (Y) and Advertisement (X)
a.
600
Advertisement (X)
We are interested in estimating the relationship between advertisements and sales in tobacco:
The OLS results follows:
b.
Tobacco Sales (Y)
C.
d.
5000
4000
3000
2000
1000
Y₁ =B₁ + B₂X₁ + u₁
t
0
0
200
Intercept
Tobbaco Ad
400
Sum of Squares Mean Square
Regression 13069027.5359 13069027.5359
Residual 27830633.2396 592141.1328
Total 40899660.7755
OLS Estimate Standard Error
2487.5635
2.6582
800
155.0608
0.5658
1000
By hand present an accurate plot of the fitted regression line, properly labeled (intercept, slope, etc.).
Predict the value of tobacco sales based on advertisement outlays equal to 900.
Consider the classical hypothesis:
Ho: B₁: = 0
Ho: B₂ = 0
H₁ : B₁ #0
H₁: B₂ #0
Perform t-tests of the above hypotheses at the 10%, 5% and 1% levels. Comment on their outcomes, and
the implications for our model of tobacco sales.
Derive the R², compute the percent of the variance of Y captured by X, and comment on how well the model
fits.
Derive 95% CI's for the intercept and slope parameters. Comment on their sizes and how they relate to the
test statistics computed above.
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