# Math 225

## Introduction to Biostatistics

### Regression Problem

Does alcoholism affect muscular strength? Fifty alcoholic men were selected from a larger study of alcoholic patients so that their ages and drinking patterns would be fairly similar. For each individual, the lifetime dose of alcohol was determined as the explanatory variable. These measurements ranged from 4 to 40 kg alcohol per kg body weight. Also, an electronic myometer was used to measure the strength of the deltoid muscle in each individual's nondominant arm. Muscular strength ranged from 10 to 30 kg. A plot of the data exhibits a weak linear relationship with no apparent nonlinearity or outliers. The output of a regression analysis is tabled below.

```Coefficients:  Value  Std. Error t value p-value
(Intercept) :  26.370  1.203     21.92   0.0000
dose : -0.29587 0.05105   -5.80   0.0000
```
(a) Give a 95% confidence interval for beta1, the slope in the "true" regression model

(strength in kg) = beta0 + beta1 (dose in kg alcohol per kg body weight)

(b) A female alcoholic who weighs considerably less than the men in the study has consumed a lifetime dose of 9 kg alcohol per kg body weight. Use the regression equation to predict the strength in her nondominant deltoid muscle.

(c) Do you think that this is a valid prediction? Explain.