Question 4) The following outputs are simple and multiple regression models for on age, triglyceride, and

weight of 40 subjects. X= age, Y= triglyceride, and Z = weight. The dependent variable is triglyceride.

The independent variables are age and weight.Using SAS outputs answer the following questions:

( each part 6 point , total 30 points)

Model 1: Age on Triglyceride

Number of Observations Read

40

Number of Observations Used

40

Analysis of Variance

Source

DF

Sumof

Squares

Mean

Square

F Value

Pr>F

Model

1

21707

21707

99.08

<.0001>

Error

38

8325.65678

219.09623

Corrected Total

39

30033

Root MSE

14.80190

R-Square

0.7228

Dependent Mean

108.15000

Adj R-Sq

0.7155

Coeff Var

13.68645

Parameter Estimates

Variable

Label

DF

Parameter

Estimate

Standard

Error

tValue

Pr>|t|

Standardized

Estimate

Intercept

Intercept

1

-1.06372

11.21894

-0.09

0.9250

0

x

Age

1

1.76864

0.17769

9.95

<.0001>

0.85017

Model 2: Weight on Triglyceride

Number of Observations Read

40

Number of Observations Used

40

Analysis of Variance

Source

DF

Sumof

Squares

Mean

Square

F Value

Pr>F

Model

1

15220

15220

39.04

<.0001>

Error

38

14813

389.82247

Corrected Total

39

30033

Root MSE

19.74392

R-Square

0.5068

Dependent Mean

108.15000

Adj R-Sq

0.4938

Coeff Var

18.25605

Parameter Estimates

Variable

Label

DF

Parameter

Estimate

Standard

Error

tValue

Pr>|t|

Standardized

Estimate

Intercept

Intercept

1

-86.72373

31.34343

-2.77

0.0087

0

z

Weight

1

0.94691

0.15154

6.25

<.0001>

0.71188

Model 3: Age and weight on Triglyceride

Number of Observations Read

40

Number of Observations Used

40

Analysis of Variance

Source

DF

Sumof

Squares

Mean

Square

F Value

Pr>F

Model

2

23695

11847

69.16

<.0001>

Error

37

6338.50089

171.31083

Corrected Total

39

30033

Root MSE

13.08858

R-Square

0.7889

Dependent Mean

108.15000

Adj R-Sq

0.7775

Coeff Var

12.10224

Parameter Estimates

Variable

Label

DF

Parameter

Estimate

Standard

Error

tValue

Pr>|t|

Standardized

Estimate

Intercept

Intercept

1

-64.19362

21.02355

-3.05

0.0042

0

x

Age

1

1.37360

0.19529

7.03

<.0001>

0.66028

z

Weight

1

0.42529

0.12487

3.41

0.0016

0.31973

a)Fit a model of triglyceride as predicted by age (write the prediction equation).

1.Prediction Equation: Triglyceride= -1.06 + 1.77 (age)

2.Prediction Equation: Triglyceride= -1.06 - 1.77 (age)

b)Fit a model of triglyceride as predicted by age and weight (write the prediction equation).

1.Prediction Equation: Triglyceride= -64.19 + 1.37 (age) + .44 (Weight)

2.Prediction Equation: Triglyceride= -64.19 - 1.37 (age) - .44 (Weight)

c)Test if your slope is significant for model 2 (weight as independent variable on Triglyceride) (H0 = beta =0).

1.Since our P value <.0001 is less than alpha .05 we reject null and conclude that the slope different from this means there linear relationship between weight triglyceride.>

2.Since our P value <.0001 is less than alpha .05 we fail to reject null and cannot conclude that the slope different from this means there no linear relationship between weight triglyceride.>

d)What is the R² and Adjusted R² from ANOVA table for model 3?

1..89

2..78

3..85

4..98

e)What would be the triglyceride someone who is 42 years old and weight 132. Use model with age and weight (Multiple regression model).

1.65.98

2.75.98

3.98.75

4.51.43

Question 4) The following outputs are simple and multiple regression models for on age, triglyceride, and weight of 40 subjects. X= age. Y= triglyceride, and Z = weight. The dependent variable is triglyceride The ind ent variables are age and weight. U SAS outputs answer the following questions: (each part 6 point , total 30 points) Model 1: Age on Triglyceride Variabl Parameter Estimate Label Parameter Standard Estimate Error t Value er > It] Standardized Estimate Number of Observations Interce Intercept 1 -1.06372 11.21894 -0.09 0.9250 Parameter Estimates Variable Label Parameter Standard Age 1 1.76864 0.17789 9.95 <.0001 df estimate error t value tandardized ec> It Estimate Number of Observations Intercept Intercept 1 -86.72373 31.34343 -2.77 0.0087 Used Weight 1 0.94691 0.15154 6.25 <.000 model weight on triglyceride analysis of variance age and f squares square value ex> F Number of Observations Read Model 21707 21707 99.08 <.0001 number of observations error used read analysis variance sum mean root mse r-square source square f value pc> F Analysis of Variance Dependent 0.7155 Model 15220 15220 39.0 <.0001 sum of mean adj r-sq error source df squares square f value pc> F oeff Var 13.68645 Corrected 30033 Model 2 23695 11847 <.0001 total error corrected be root mse r-square dependent mean adj r-sq coeff var r- square e what would the triglyceride someone who is years old and weight use model with age regression parameter estimates variable label estimate standard tvalu standardize intercept fit a of as predicted by prediction equation equation: triglyceride_ diction b . .44 test if your slope significant for independent on since our p value less than alpha .05 we reject null conclude that ans there linear relation different from this means relationship between triglyceride. fail to cannot no d r adjusted anova table>