THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION

question 72

Essay

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
Given a simple regression analysis,suppose that we have obtained the fitted regression model:
_i = 6 + 8x_i and also the following statistics: s_e = 3.20,
= 8,n = 42,and
-A scatter diagram includes the data points (x = 2,y = 5),(x = 4,y = 12),(x = 6,y = 20),(x = 8,y = 28),and (x = 10,y = 30).Two regression lines are proposed: (1)
= -0.6 + 3x,and (2)
= -1 + 5x.Using the least squares criterion,which of these regression lines is the better fit to the data? Why?

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Definitions:

T-table

A table used in statistics to determine critical values for the t-distribution, useful for hypothesis testing or setting confidence intervals.

Degrees Of Freedom

The number of independent values or quantities which can be assigned to a statistical distribution or a system without violating any constraint.

F Table

A chart used in statistics that provides critical values for the F-distribution, helpful in analyzing variances by comparing the ratio of two sets of data.

Degrees Of Freedom

The number of independent values in a statistical calculation that can vary without violating the calculation's constraints.