Question

Let the response y be rest (resting heart rate), and covariates x1 be height in inches (hgt), x2 be weight in pounds (wgt), and x3 smoking status (smoke, 1 for smokers and 0 for non-smokers).

a) Correlation analysis
b) Regression analysis
c) Descriptive statistics
d) Inferential statistics

Answer 1

b) Regression analysis is optimal for understanding how height, weight, and smoking status impact resting heart rate, providing detailed insights through coefficient estimation and model assessment. Thus B is the correct option.

Step-by-step explanation:

Regression analysis is the most appropriate statistical method for examining the relationship between the response variable (resting heart rate,
`\(y\))` and the covariates
`(height in inches, \(x_1\)`, weight in pounds,
`\(x_2\)`, and smoking status,
`\(x_3\))`. It helps us understand how changes in the covariates are associated with changes in the resting heart rate.

In this scenario, the multiple regression analysis can be employed, considering more than one predictor variable simultaneously. The model can be expressed as:

`\[ y = \beta_0 + \beta_1x_1 + \beta_2x_2 + \beta_3x_3 + \epsilon \]`

Here,
`\(\beta_0\)` is the intercept, and
`\(\beta_1, \beta_2, \beta_3\)` are the coefficients for the corresponding covariates. The error term
`(\(\epsilon\))` accounts for unobserved factors influencing the resting heart rate.

Regression analysis allows us to estimate the impact of each covariate on the response variable, assess the overall model fit, and make predictions. It goes beyond correlation analysis by providing insights into the strength and direction of the relationships, offering a more comprehensive understanding of the factors influencing resting heart rate.