# Bivariate data

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Bivariate data obtained for the paired variables and are shown below, in the table labelled "Sample data." These data are plotted in the scatter plot in Figure 1, which also displays the least-squares regression line for the data. The equation for this line is .

In the "Calculations" table are calculations involving the observed values, the mean of these values, and the values predicted from the regression equation.

Sample data

X Y

73.2

70.3

61.6

63.2

60.2

Calculations

^ 2 ^ - 2 - 2

(y-y) (y - y) (y - y)

0.4543 46.5943 56.2500

0.6593 14.3489 21.1600

20.0525 0.1429 16.8100

1.4738 13.7938 6.2500

0.0392 32.4672 30.2500

22.6791 107.3471 130.7200

Answer the following:

1. The least-squares regression line given above is said to be a line which "best fits" the sample data. The term "best fits" is used because the line has an equation that minimizes the ____

a. total sum of squares

b. regression sum of squares

c. error sum of squares

which for these data is ___

a. 130.7200

b. 107.3471

c. 22.6791

2. The variation in the sample y values that is explained by the estimated linear relationship between x and y is given by the ___

a. total sum of squares

b. regression sum of squares

c. error sum of squares

which for these data is ___

d. 130.7200

e. 107.3471

f. 22.6791

2

3. The value r is the proportion of total variation in the sample y values that is explained by the estimated linear relationship between x and y. For these data, the value of 2

r

is ___ (Round your answer to at least two decimal places)

4. For the data point (70.7, 63.2), the value of the residual is ___ (Round your answer to at least 2 decimal places.

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1. The least-squares regression line given above is said to be a line which "best fits" the sample data. The term "best fits" is used because the line has an equation that minimizes the ____

a. total sum of squares

b. regression sum of squares

c. error sum of squares

*by the definition of OLS regression, the line has an equation that minimizes the error sum of squares.

which for these ...

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