\"A producer of various feed additives for cattle conducts a study of the number

Question

"A producer of various feed additives for cattle conducts a study of the number of days of feedlot time required to bring beef cattle to market weight. Eighteen steers of essentially identi- cal age and weight are purchased and brought to a feedlot. Each steer is fed a diet with a specic combination of protein content, antibiotic concentration, and percentage of feed supplement. The data are as follows:

1. For steer #3, Calculate the predicted feedlot time and the residual.

2. Write the residual standard deviation and interpret.

3. Give a 95% confidence interval for 1. Interpret your confidence interval

Explanation / Answer

Here supplement time is dependent variable and protein content, antibiotic concentration are independent variables.

This is problem of multiple regression.

We can do multiple regression in MINITAB.

steps :

ENTER data into MINITAB sheet --> STAT --> Regression --> Regression --> Response : supplem time --> Predictors : select anibio and protein --> Options --> Prediction intervals for new observations : 1 7 --> Click on prediction limit --> ok --> Results : select second option --> ok --> ok

Regression Analysis: Supplem time versus anibio, protein

The regression equation is
Supplem time = 90.2 - 1.38 anibio - 4.00 protein

Predictor Coef SE Coef T P
Constant 90.208 4.229 21.33 0.000
anibio -1.3750 0.5884 -2.34 0.034
protein -4.000 1.922 -2.08 0.055

S = 4.076 R-Sq = 39.5% R-Sq(adj) = 31.4%

Analysis of Variance

Source DF SS MS F P
Regression 2 162.75 81.38 4.90 0.023
Residual Error 15 249.25 16.62
Total 17 412.00

Predicted Values for New Observations

New Obs Fit SE Fit 95.0% CI 95.0% PI
1 60.833 10.870 ( 37.664, 84.003) ( 36.088, 85.578) XX
X denotes a row with X values away from the center
XX denotes a row with very extreme X values

Values of Predictors for New Observations

New Obs anibio protein
1 1.00 7.00

Lack of fit test
Possible curvature in variable protein (P-Value = 0.020)
Overall lack of fit test is significant at P = 0.020

Here we can see that model is significant since p-value for the overall model is 0.023 which is less than 0.05.

Protein is insignificant variable while anibio is significant variable.

1. For steer #3, Calculate the predicted feedlot time and the residual.

We have to find predicted value for anibio = 7 and protein = 1

This we can find using regression equation.

Supplem time = 90.2 - 1.38 anibio - 4.00 protein

Supplem time = 90.2 - 1.38 * 7 - 4.00 *1 = 76.54

But observed value for steer is 81.

Residual = 81 - 76.54 = 4.46

2. Write the residual standard deviation and interpret.

S = 4.076

S represents the average distance that the observed values fall from the regression line. Conveniently, it tells you how wrong the regression model is on average using the units of the response variable. Smaller values are better because it indicates that the observations are closer to the fitted line.

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