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Chapter 4: Q.4.5 (page 174)

a. Find the regression equation for the data points, use the defining formulas in definition 4.4 to obtain sxxandsxy

b. Graph the regression equation and the data points

Short Answer

Expert verified

(a)y^=1+2x

(b)

Step by step solution

01

Part(a) Step 1:Given Information   

The given data is :

We have to determine the regression equation

02

Part (a) Step 2: Explanation  

The regression equation is :

y^=b0+b1x

where,

b0=sxysxx

b1=y-b1x

The table can be obtained as:

x炉=鈭�xn=2

y=鈭�yn=5

sxx=10

sxy=20

Therefore,

b1=2

b0=1

Therefore, the regression equation will be

y^=b0+b1x=1+2x

03

Part (b) Step 1 :Given Information  

The given data is:

We have to determine the graph of regression equation and data

04

Part (b) Step 2: Explanation   

The regression equation and data points can be drawn on graph as:

Thus, the regression equation will be:y^=1.00+2.00x

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Most popular questions from this chapter

The coefficient of determination of a set of data points is 0.70yand the slope of the regression line is -3.58. Determine the linear correlation coefficient of the data.

Graduation Rates. Graduation rate-the percentage of entering freshmen attending full time and graduating within 5 years and what influences it is a concern in U.S. colleges and universities.

US News and World Report's "College Guide" provides data on graduation rates for colleges and universities as a function of the per centage of freshmen in the top 10% of their high school class, total spending per student, and student-to-faculty ratio. A random sample of 10 universities gave the following data on student-to-faculty ratio (S/F ratio) and graduation rate (Grad rate).

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c. Determine the regression equation for the data, and draw its graph

on the scatterplot you drew in part (a).

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ratio and graduation rate.

e. What does the slope of the regression line represent in terms of student-to-faculty ratio and graduation rate?

f. Use the regression equation to predict the graduation rate of a university having a student-to-faculty ratio of 17.

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