## 6 Item 6 For a specific species of fish in a pond, a wildlife biologist wants to build a regression equation to predict the weight of a fish

6 Item 6 For a specific species of fish in a pond, a wildlife biologist wants to build a regression equation to predict the weight of a fish based on its length. The biologist collects a random sample of this species of fish and finds that the lengths vary from 0.75 to 1.35 inches. The biologist uses the data from the sample to create a single linear regression model. Would it be appropriate to use this model to predict the weight of a fish of this species that is 3 inches long

## Answers ( )

Answer:Yes, because the regression equation is based on the random sample.

Step-by-step explanation:A simple linear regression model that describes the relationship between X and Y takes the form

Yi= ∝ + βXi + εi or

Y i= U(y.x) + εi

where εi’s are the random errors. The random errors εi’s are assumed to be independent of Xi and normally distributed with E(εi)= 0 and Var (εi)= σ²(y.x) , a constant for all Xi. These assumptions imply that Yi also have a common variance σ²(y.x) , as the only random element in the is εi.

The estimated regression line Y= a+ bX is also the predictor of Yi= ∝ + βXi+ εi

. That is Y^ can also be used to predict an individual value Y0 of Yi rather than a mean value, corresponding to the given X0. To draw the inferences about Y0 we need to know it mean and variance.