An Experiment Was Performed on a Certain Metal to Determine $\hat { y }$

question 148

Essay

An experiment was performed on a certain metal to determine if the strength is a function of heating time.Partial results based on a sample of 10 metal sheets are given below.The simple linear regression equation is $\hat { y }$ = 1 + 1x .The time is in minutes and the strength is measured in g/cm².You are also given the following sample statistics:
MSE = 0.5, $\sum X$ = 30, $\sum X ^ { 2 }$ = 104.
-Predict the strength when heating time is 3 minutes.

---

Definitions:

Regression Line

A line that best fits the data points in a scatter plot, showing the relationship between two variables.

Variation

The extent to which data points in a statistical distribution or data set diverge from the average or mean.

Coefficient of Determination

A statistical measure, usually represented as R^2, that indicates the proportion of variance in the dependent variable predictable from the independent variables.

Correlation Coefficient

A statistical measure that calculates the strength of the relationship between two variables.