Question12) 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:

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 Standard tValue Pr>|t] Standardized

Estimate Error 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 Standard tValue Pr>|t| Standardized

Estimate Error 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 Standard tValue Pr>|t|Standardized

Estimate Error 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 is different from 0. This means there is linear relationship between weight and triglyceride.

2.Since our P value <.0001 is less than alpha .05 we fail to reject null and cannot conclude that the slope is different from 0. This means there is no linear relationship between weight and 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