Question

A 2-column table with 6 rows. The first column is labeled miles driven with entries 27, 65, 83, 109, 142, 175. The second column is labeled gallons in tank with entries 13, 12, 11, 10, 9, 8. Janelle tracks the number of miles she drives and the number of gallons of gas she has left. What is the linear regression model for this scenario? What is the correlation coefficient? What is the strength of the model?

Answer 1

Answer:

linear regression answer : y = -0.035x + 13.989

correlation coefficient : -0.996

strength : strong negative

Step-by-step explanation:

trust me bro i know its right

Answer 2

Answer:

1) The linear regression model is y = -0.0348·x + 13.989

2) The correlation coefficient is -0.0725

3) The strength of the model is strong - association

Step-by-step explanation:

1)

                         X            Y          XY       X²

                         27            13           351          729

                         65             12          780         4225

                         83              11          913         6889

                         109            10          1090      11881

                         142            9            1278     20164

                         175              8           1400      30625

                ∑      601              63 5812 74513

From y = ax + b, we have

$a = \frac{n\sum xy - \sum x\sum y }{n\sum x^{2}-\left (\sum x \right )^{2}} = \frac{6 \times 5812 - 601 \times 63}{6 \times 74513-601^{2}} = - 0.0348$

b = 1/n(∑y -a∑x) = 1/6(63 - (0.0348)×601) = 13.989

Therefore, the linear regression model is y = -0.0348·x + 13.989

2)

$r = \frac{n\sum xy - \sum x\sum y }{\sqrt{[n\sum x^{2}-\left (\sum x \right )^{2}] [n\sum y^{2}-\left (\sum y \right )^{2}]}} = \frac{6 \times 5812 - 601 \times 63}{\sqrt{[6 \times 74513-601^{2}] [6 \times 3969 - 63^2]} } = - 0.0725$

3) The strength is - association.