Question

A series of experiments have been carried out to determine the relationship between the operating temperature and the lifetime of a particular product.

A linear regression model is fitted to the data and R^2=0.92. Using this model, it is predicted that the product will last 58.3 hours when running at a temperature of 80°C. Would you be confident in this prediction?

A.Only if the true value is included in the confidence interval.

B Only if a temperature of 80°C is within the experimental range.

C. Yes, since the model provides an excellent fit to the data based on the R2 value

D. No, since this is not statistically significant at the 5% level.

Answer 1

A series of experiments have been carried out to determine the relationship between the operating temperature and the lifetime of a particular product.

A linear regression model is fitted to the data and R^2=0.92.

Coefficient of determination is 0.92

ie 92% of the variation in the lifetime of a particular product is explained by the model.

So the model is very good fitted.

Using this model, it is predicted that the product will last 58.3 hours when running at a temperature of 80°C. Would you be confident in this prediction?

We can say it is a good prediction because the R^2 value is near to 1.so it denotes a good fit to the data.

Answer:-

C. Yes, since the model provides an excellent fit to the data based on the R2 value