Annual high temperatures in a certain location have been tracked for several years. let xx represent the year and yy the high temperature. based on the data shown below, calculate the correlation coefficient (to three decimal places) between xx and yy. use your calculator! x y4 43.655 40.746 38.537 37.228 33.019 30.610 29.8911 27.1812 25.8713 23.5614 22.2515 18.6416 18.3317 16.9218 13.8119 9.9

r =-0.996

Step-by-step explanation:

The correlation coefficient is a "statistical measure that calculates the strength of the relationship between the relative movements of two variables". It's denoted by r and its always between -1 and 1.

In order to calculate the correlation coefficient we can begin doing the following table:

n     x         y        xy         x*x       y*y

1     4      43.65  174.6       16     1905.323

2     5     40.74  203.7      25    1659.748

3     6     38.53  231.18      36   1484.561

4     7     37.22  260.54    49    1385.323

5     8     33.01   264.08    64   1089.660

6     9     30.61   275.49    81    936.972

7     10    29.89  298.9     100  893.412

8     11     27.18   298.98   121   738.752

9     12    25.87  310.44    144   669.257

10    13    23.56  306.28   169  555.0974

11     14    22.25  311.50     196  495.063

12    15    18.64   279.60   225  347.450

13    16    18.33   293.28   256  335.989

14    17    16.92   287.64   289  286.286

15    18    13.81    248.58   324  190.716

16    19    9.9       188.10    361   98.01

n=16  

And in order to calculate the correlation coefficient we can use this formula:

So then the correlation coefficient would be r =-0.996

(-2,3)

Step-by-step explanation:

Step 1. Isolate x for 3x + 5y = 9

3x + 5y - 5y = 9 - 5y

3x = 9 - 5y

3x/3 = 9/3 - 5y/3

x= (9-5y)/3

Step 2. Simplify

-3*((9-5y)/3) + 3y = 15

-3*((9-5y)/3) = 9 - 5y = -(-5 + 9) + 3y

-9+5y+3y

-9+8y = 15

Step 3 Isolate y for -9+8y=15

-9+8y+9=15+9

8y=24

8y/8 = 24/8

y=3

Step 4 Substitute y = 3

x = (9-5*3)/3

-(6/3) = (-2)

x = -2