Question

for the quantitative variables

x

and

y

are given in the table below. These data are plotted in the scatter plot shown next to the table.

In the scatter plot, sketch an approximation of the least-squares regression line for the data.

x

y

7.4

6.6

4.0

5.0

2.0

3.9

3.1

5.0

9.4

8.4

4.7

5.9

6.6

6.2

8.5

6.9

7.9

7.3

1.6

3.7

4.4

4.6

2.8

3.9

2.7

3.1

5.7

6.3

5.9

7.3

9.7

8.3

6.9

6.3

8.8

8.4

x 1 2 3 4 5 6 7 8 9 10 11 y 1 2 3 4 5 6 7 8 9 10 11

Answer 1

(a) The step-by-step instructi ons to obtain Regression

output using Minitab 18:

* Store the variables (X) in the columns of

the Mnitab18 worksheet

* Choose Regression *Regression *Fittted Line Plot

* Select the variable (Y) in the Responses box and then select the

variable (X) in the Continuous Predictors box

* Cli Ck ok

The simple linear regressl on equation plotted on the scatter plot

using the technology:

The scatterplot enables that the measure of the linear relationship between the two quantitative variables x and y. The linear relationship between the two variables is positive, since the direction of fitted line is upwards. The value of the coefficient of determination is R²=24.9% indicates the percentage of variation in the dependent variable can be explained by the independent variable. The adjusted R²=20.2% is less than that of the R² value observed in the fitted line plot.