Test the global significance of full model applied to data

Assignment Help Applied Statistics

Reference no: EM132352704

Assignment - Answer all questions.

Instructions: You must use SAS to obtain appropriate analyses of the data where required and use the SAS output obtained in answering the questions that follow the problem statement. Use a 5% level of significance (α = 5%) where appropriate unless otherwise specified. (Use 3 decimal places in your calculations and answers). You must also submit your SAS program file.

The Problem - Air Pollution

A climatologist is interested in predicting air quality in cities in the USA. Air quality is measured by the mean concentration of sulphur dioxide (SO₂) in the air. Information pertaining to 7 (possible) explanatory variables was gathered over a 3-year period. Full data was collected for 41 US cities.

Data collected:

Sulphur dioxide (SO₂)	Average sulphur dioxide content of the air in micrograms per cubic metre.
Temp	Average annual temperature in degrees Fahrenheit
Factory	Number of manufacturing enterprises employing 20 or more workers
Pop	Population in thousands in 1999
Wind	Average annual wind speed
Precip	Average annual precipitation in inches
Dayrain	Average number of days with precipitation per year
Dust	Average concentration of dust particles in ppm (parts per million)

The data is available on Canvas as 'Pollution.txt'.

Use SAS to run a full multiple linear regression analysis on the data, in order to answer the questions that follow.

Questions -

(i) Copy the ANOVA table for the full model into the table below. Explain how the degrees of freedom for each component of variation is calculated.

Source	df	Sum of squares	Mean square	F
Model
Error
Total

(ii) Use an F test to test the global significance of the full model applied to the data, include your hypothesis, test statistics (i.e. F and critical F) and your full conclusion.

(iii) State the value of the coefficient of determination for the full model and explain how it relates to the SSError.

(iv) Examine the SAS output and test the significance of each of the individual explanatory variables. You should include your hypotheses, and explain how you have drawn your conclusions.

(v) Use a stepwise procedure to obtain the optimal (best fit) model. State the least squares estimate of this model, explaining each of the terms in your model.

(vi) State and describe how you would interpret the R², adj R² and C_p statistics to identify the optimal model obtained in part (iv).

(vii) Use the optimal model to predict SO₂ for a city where the average temperature is 60.7^oF, there are 350 enterprises with 20 or more workers, a population of 580000, average wind speed of 9.5, average precipitation of 30.0 inches, 150 days of rain on average and a dust concentration of 7.0 ppm. State and interpret the 95% prediction interval for this city.

(viii) Explain how you would calculate residuals for the optimal model. You may obtain and use residuals from the SAS output to aid your explanation.

(ix) Use the residual plots provided in the SAS output to assess the validity of assumptions that underlie the model. Refer specifically to the distribution of the residuals, the mean of the residuals and homoscedasticity.

Reference no: EM132352704

Questions Cloud

Diverse microorganisms that cause no harm : The skin is the human body's largest organ. It is colonized by diverse microorganisms that cause no harm to their host

Ratio analysis on the financial statements : Now that you have their financial information I would like you to perform a ratio analysis on the financial statements. Focus on financial statement analysis.

What quantity would maximize profits for the firm : What quantity would maximize profits for this firm? (Hint: Recall that profit maximizing is where MR = MC). At what price should this firm sell its product.

Explain how oxidation of a substrate proceeds without oxygen : Explain how oxidation of a substrate proceeds without oxygen? Does this involve glycolysis?

Test the global significance of full model applied to data : Use an F test to test the global significance of the full model applied to the data, include your hypothesis, test statistics (i.e. F and critical F)

What characteristics do you observe in the industry : What characteristics do you observe in the industry that support this identification? Provide evidence. What does the market type suggest about pricing.

Briefly discuss pros and cons of the merger : Briefly discuss pros and cons of the merger (effect on the industry, effect on consumers) based on the following: market concentration.

Composed of charged colored ions : Most stains used in microbiology are usually salts, or sometime acids or bases, composed of charged colored ions. The colored ions are called chromophores

Discuss non-price competition within the industry : Discuss non-price competition within the industry. Describe the bargaining power of the company's suppliers and buyers. Describe the long-run goals of company.

Reviews

len2352704

8/5/2019 11:44:01 PM

You are required to answer all questions on the test paper provided, this should be submitted via Canvas. Instructions: You must use SAS to obtain appropriate analyses of the data where required and use the SAS output obtained in answering the questions that follow the problem statement. Use a 5% level of significance where appropriate unless otherwise specified. (Use 3 decimal places in your calculations and answers). Show all calculations. Answer all questions in the spaces provided. You must also submit your SAS program file on Canvas.

Write a Review

Required(*) Message

User Account

All Pages