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.   y=____+______x (Round to two decimal places as​ needed.)​   2. Identify a characteristic of the data that is ignored by the regression line.   A.There is no trend in the data.   B.The data has a pattern that is not a straight line.   C.There is an influential point that strongly affects the graph of the regression line.   D.There is no characteristic of the data that is ignored by the regression line.

.   y=____+______x (Round to two decimal places as​ needed.)​   2. Identify a characteristic of the data that is ignored by the regression line.   A.There is no trend in the data.   B.The data has a pattern that is not a straight line.   C.There is an influential point that strongly affects the graph of the regression line.   D.There is no characteristic of the data that is ignored by the regression line.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter4: Equations Of Linear Functions
Section4.6: Regression And Median-fit Lines
Problem 4PPS
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​1.   y=____+______x (Round to two decimal places as​ needed.)​
 
2. Identify a characteristic of the data that is ignored by the regression line.
 
A.There is no trend in the data.
 
B.The data has a pattern that is not a straight line.
 
C.There is an influential point that strongly affects the graph of the regression line.
 
D.There is no characteristic of the data that is ignored by the regression line.
Use the given data to find the equation of the regression line. Examine the scatterplot and identify a characteristic of the data that is ignored by the regression line. 7 13 12 11 3 5 10 4 8 У 8.05 8.31 9.25 8.96 9.34 2.31 7.04 5.74 9.44 4.16 8.80 %3D + x (Round to two decimal places as needed.)
Transcribed Image Text:Use the given data to find the equation of the regression line. Examine the scatterplot and identify a characteristic of the data that is ignored by the regression line. 7 13 12 11 3 5 10 4 8 У 8.05 8.31 9.25 8.96 9.34 2.31 7.04 5.74 9.44 4.16 8.80 %3D + x (Round to two decimal places as needed.)
Expert Solution
Answer

We have used the excel data analysis tool to run the regression analysis.

x y (x-xbar) (x-xbar)^2 (y-ybar) (y-ybar)^2 (x-xbar)*(y-ybar)
7 8.05 -1 1 0.65 0.4225 -0.65
13 8.31 5 25 0.91 0.8281 4.55
9 9.25 1 1 1.85 3.4225 1.85
12 8.96 4 16 1.56 2.4336 6.24
11 9.34 3 9 1.94 3.7636 5.82
3 2.31 -5 25 -5.09 25.9081 25.45
6 7.04 -2 4 -0.36 0.1296 0.72
5 5.74 -3 9 -1.66 2.7556 4.98
10 9.44 2 4 2.04 4.1616 4.08
4 4.16 -4 16 -3.24 10.4976 12.96
8 8.8 0 0 1.4 1.96 0

 

The slope is given by

\beta_{1}= \frac{\sum (x - \overline{x})(y - \overline{y})}{\sum (x - \overline{x})^2}

\beta_{1}=\frac{66}{110} =0.6

 

The intercept is given by

\beta_{0} = \overline{y} -\beta_{1}\overline{x}

\beta_{0} = 7.4-8\times 0.6= 2.6​​​​​​​

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