# Important information about Bivariate Data

Please label your answers in bold and away from any calculations.

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

0.9 1.1

1.8 2.0

2.7 2.6

3.8 3.0

5.2 5.5

Calculations

- ^ ^ -

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

3.0276 0.0180 3.5119

0.7056 0.0353 1.0568

0.0576 0.0034 0.0331

0.0256 0.4789 0.7259

7.0756 0.2421 4.7002

--------- ---------- ----------

10.8920 0.7776 10.0279

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. error sum of squares

b. total sum of squares

c. regression sum of squares

(continued), which for these data is _____

a. 0.7776

b. 10.8920

c. 10.0279

2. For the data point (5.2, 5.5), the value of the residual is ____. (Round your answer to at least two decimal places.)

3. The total variation in the sample y values is given by the _____,

a. error sum of squares

b. total sum of squares

c. regression sum of squares

(continued), which for these date is _____

a. 0.7776

b. 10.8920

c. 10.0279

2

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

2

of r is ______ (Round your answer to at least 2 decimal places.)

https://brainmass.com/statistics/regression-analysis/important-information-about-bivariate-data-13198

#### Solution Summary

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

0.9 1.1

1.8 2.0

2.7 2.6

3.8 3.0

5.2 5.5

Calculations

- ^ ^ -

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

3.0276 0.0180 3.5119

0.7056 0.0353 1.0568

0.0576 0.0034 0.0331

0.0256 0.4789 0.7259

7.0756 0.2421 4.7002

--------- ---------- ----------

10.8920 0.7776 10.0279

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. error sum of squares

b. total sum of squares

c. regression sum of squares

(continued), which for these data is _____

a. 0.7776

b. 10.8920

c. 10.0279

2. For the data point (5.2, 5.5), the value of the residual is ____. (Round your answer to at least two decimal places.)

3. The total variation in the sample y values is given by the _____,

a. error sum of squares

b. total sum of squares

c. regression sum of squares

(continued), which for these date is _____

a. 0.7776

b. 10.8920

c. 10.0279

2

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

2

of r is ______ (Round your answer to at least 2 decimal places.)