# Bivariate Data explained in this solution

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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

56.3 73.4

60.8 72.9

64.5 61.5

69.2 65.8

75.8 62.5

Calculations

^ - 2 ^ 2 - 2

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

26.8946 0.9880 38.1924

6.6358 9.6348 32.2624

0.1849 37.8225 32.7184

5.2716 0.7674 2.0164

37.5034 1.9712 22.2784

76.4903 51.1839 127.4680

Answer the following:

1. The total variation in the sample y values is given by the ____

a. total sum of squares

b. error sum of squares

c. regression sum of squares

which for these data is ___

a. 127.4680

b. 51.1839

c. 76.4903

2. The proportion of the total variation in the sample y values can be explained by the estimated linear relationship between x and y is___ (Round your answer to at least two decimal places.)

3. For the data point (75.8, 62.5), the value of the residual is ___ (Round your answer to at least two decimal places.)

4. 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. error sum of squares

c. regression sum of squares

which for these data is ___

a. 127.4680

b. 51.1839

c. 76.4903

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The expert analyzes bivariate data of a solution. The solution answers the question(s) below.

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1. *The total sum of squares(TSS)= SUM((y - Mean(y))^2).

2.

*R squared is the proportion of ...

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