What the null and alternative hypotheses that will be tested

Assignment Help Basic Statistics
Reference no: EM13917063

A biologist conducted an experiment to study the effect that various characteristics of a stream have on the amount of fish biomass that the stream supports. The regressor variables are as follows:

X1: average depth of stream
X2: area of instream cover (i.e., undercut banks, logs, boulders, etc.)
X3: percent canopy cover
X4: amount of surface area ≥ 25 cm in depth.

The response variable is y, the fish biomass.

Data file: biomass.

biomass

depth

cover

percent

area

100

14.3

15

12.2

48

388

19.1

29.4

26

152.2

755

54.6

58

24.2

469.7

1288

28.8

42.6

26.1

485.9

230

16.1

15.9

31.6

87.6

0

10

56.4

23.3

6.9

551

28.5

95.1

13

192.9

345

13.8

60.6

7.5

105.8

0

10.7

35.2

40.3

0

348

25.9

52

40.3

116.6

(a) Fit the full model with all 4 regressor variables to these data. Find S2 and R2 .

(b) Perform the overall F-test for this model, explicitly stating the null and alternative hypotheses corresponding to this F-test, and state your conclusions.

(c) Compute t-statistics used to test whether each of the regression coefficients in this model individually is equal to zero, and state your conclusions.

(d) Now fit the model y = b0 + b2X2 + b2X4+ e. If we define this model as the "reduced model" and the model in part (a) as the "full model", what are the null and alternative hypotheses that will be tested by the F-test corresponding to the ANOVA whose residual SS is that from the full model and whose total SS is the residual SS from the reduced model? Perform this test and state your conclusions.

Please include R or SAS code, if you use Minitab, include the procedure and answer each question carefully, not just a report like

SUMMARY OUTPUT

















Regression Statistics








Multiple R

0.981117








R Square

0.96259








Adjusted R Square

0.932662








Standard Error

101.6917








Observations

10

















ANOVA









df

SS

MS

F

Significance F




Regression

4

1330434

332608.6

32.16344

0.000922




Residual

5

51706.01

10341.2






Total

9

1382141

 

 

 













Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Lower 95.0%

Upper 95.0%

Intercept

85.75037

125.1932

0.684944

0.523834

-236.069

407.5698

-236.069

407.5698

depth

-15.9333

5.142993

-3.09807

0.026912

-29.1538

-2.71286

-29.1538

-2.71286

cover

2.422796

1.6482

1.469965

0.201524

-1.81404

6.659628

-1.81404

6.659628

percent

1.827536

3.292229

0.555106

0.60274

-6.63541

10.29048

-6.63541

10.29048

area

3.073792

0.373856

8.221853

0.000433

2.112764

4.03482

2.112764

4.03482




























RESIDUAL OUTPUT

















Observation

Predicted biomass

Residuals

Standard Residuals






1

64.08349

35.91651

0.473854






2

368.0009

19.99915

0.263853






3

844.2986

-89.2986

-1.17814






4

1271.336

16.66447

0.219858






5

194.7604

35.23964

0.464924






6

126.8534

-126.853

-1.6736






7

478.7505

72.2495

0.953203






8

351.6054

-6.60541

-0.08715






9

74.19573

-74.1957

-0.97888






10

231.1161

116.8839

1.542075















Reference no: EM13917063

Questions Cloud

How does the length of the wing of the helicopter affect : How does the length of the wing of the helicopter affect it's time to reach the ground and how does jelly's density affect the refractive index of a laser
What is a wiki and what are its advantages to businesses : What is a wiki, and what are its advantages to businesses? Name a few of the potential risks that social networking sites may pose to business.
The plates perpendicular to the electric field : A 150-V battery is connected across two parallel metal plates of area 28.5 cm2 and a separation of 8.20 mm. A beam of alpha particles (charge +2e, mass 6.64E-27 kg) is accelerated from rest through a potential difference of 1.75 kV and enters the reg..
Manufacturing overhead : Knight Company reports the following costs and expenses in May.From the information, determine the total amount of:Manufacturing overhead
What the null and alternative hypotheses that will be tested : Now fit the model y = b0 + b2X2 + b2X4+ e. If we define this model as the "reduced model" and the model in part (a) as the "full model", what are the null and alternative hypotheses that will be tested by the F-test corresponding to the ANOVA whos..
Analyze the fundamentals of pki : You are the Information Security Officer at a small software company. The organization currently utilizes a Microsoft Server 2008 Active Directory domain administered by a limited number of over-tasked network administrators.
What internet behavior could get employees fired : What Internet behavior could get employees fired? Do employees deserve broad Internet access on the job-if they are responsible? Should employers block access to Web sites?
Find the maximum velocity for the overturn of a car moving : Find the maximum velocity for the overturn of a car moving on a circular track of radius 100 m. The co-efficient of friction between the road and tyre is 0.2
Account Receivable : The Net sale is 350000.00 and the Account Receivable is 53,0000 on 2015

Reviews

Write a Review

 

Basic Statistics Questions & Answers

  In how many ways make bonuses greater than given value

Bonus is sales are made to 3 of the neighbors, and $200 if he able to sell to 4 neighbors. In how many ways can edwards make bonuses greater than $50?

  Determining multiple determination

You decide to predict gasoline prices in different cities and towns in the U.S. for your term project. Your dependent variable is price of gasoline per gallon and your explanatory variables are per capita income

  Applied business statistics test

The following data represent scores of 50 students in the applied business statistics test. Prepare the frequency distribution table and the frequency histogram for this data set.

  The probability density function of the net weight in

the probability density function of the net weight in pounds of a packaged chemical herbicide is fx 2.0 for 49.75 lt

  The frequency distribution below shows the distribution for

refer to the following frequency distribution for questions 1 2 3 and 4.the frequency distribution below shows the

  Find the probability that the third job with fatal errors

some jobs submitted for processing on a particular cpu have fatal programming errors while others do not. suppose that

  Standard deviation-new cardholders expect to default

How many of these new cardholders would you expect to default? What is the standard deviation?

  Let a b and c be independent random variables uniformly

let a b and c be independent random variables uniformly distributed over 04 03 and 06 respectively. what is the

  Express the probability as a decimal

Express the probability as a decimal

  Anova for mean weight

The weights (in grams) of four different colors of M&M candies are given below, along with the mean weight and variance of each color, and the variance of the sample means.

  Find the weighted mean for three exams if the first one was

find the weighted mean for three exams if the first one was worth 20 and the student received a 80 the second was

  Find examination score of the population of examinations

The average score in the sample was 84 with a variance of 12.25. The 95% confidence interval for the average examination score of the population of the examinations is?

Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd