Question

question #5
when running a regression consisting of 20 data points, the linear regression coefficient was r = .811. does there appear to be a relationship? use α = 0.01.
critical values of the pearson
correlation coefficient r
n | α = .05 | α = .01
4 | .950 | .999
5 | .878 | .959
6 | .811 | .917
7 | .754 | .875
8 | .707 | .834
9 | .666 | .798
10 | .632 | .765
11 | .602 | .735
12 | .576 | .708
13 | .553 | .684
14 | .532 | .661
15 | .514 | .641
16 | .497 | .623
17 | .482 | .606
18 | .468 | .590
19 | .456 | .575
20 | .444 | .561
25 | .396 | .505
30 | .361 | .463
35 | .335 | .430
40 | .313 | .402
45 | .294 | .378
50 | .279 | .361
60 | .254 | .330
70 | .236 | .305
80 | .220 | .286
90 | .207 | .269
100 | .196 | .256
○ no, because .811 > .207.
○ yes, because .811 > .207.
○ yes, because .811 > .561.
○ no, because .811 > .561.

Explanation:

Step1: Find critical value

For \( n = 20 \) and \( \alpha = 0.01 \), from the table, the critical value is \( 0.561 \).

Step2: Compare \( r \) and critical value

We have \( r = 0.811 \). Since \( 0.811>0.561 \), we reject the null hypothesis (no relationship) and conclude there is a relationship.

Answer:

Yes, because.811 >.561.