Use the given data set to complete parts (a) through (c) below. (Use a = 0.05.) 10 8 13 11 14 6 4 12 7 7.45 6.76 12.75 7.11 7.81 8.85 6.08 5.39 8.16 6.42 5.72 Click here to view a table of critical values for the correlation coefficient. A Table of Critical Values - X a. Construct a scatterplot. Choose the correct graph below. OA. O B C. AY 16- Ay 16- Q Ay 16- a = .05 a = 01 12- 12- 12- 4 .950 .990 8- 8- 8- ....... 878 .959 4- 4- 4- 6 811 .917 .754 875 12 16 8 12 16 8. 707 .834 9. .666 798 b. Find the linear correlation coefficient, r, then determine whether there is sufficient evidence to support the claim of a linear correlation between the two variables. 10 .632 .765 The linear correlation coefficient is r=O .602 11 .735 12 .576 .708 (Round to three decimal places as needed.) 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 40 312 402 45 294 .378 50 279 361 60 254 330 70 236 .305 80 220 286 90 207 269 100 196 256 NOTE: To test Hop = 0 against H: p* 0, reject Ho if the absolute value of r is greater than the critical value in the table
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
![Use the given data set to complete parts (a) through (c) below. (Use a= 0.05.)
10
8
13
11
14
6
4
12
7
y
7.45
6.76
12.75
7.11
7.81
8.85
6.08
5.39
8.16
6.42
5.72
Click here to view a table of critical values for the correlation coefficient.
Table of Critical Values
a. Construct a scatterplot. Choose the correct graph below.
OA.
OB.
Ay
16-
A
16-
16-
a = .05
a = .01
12-
12-
12-
4.
.950
.990
8-
8-
8-
5
.878
.959
4-
...
4-
4-
6
.811
.917
0-
.875
0-
4
0-
754
12 16
12
16
4
8
12
16
.834
.798
8
.707
.666
b. Find the linear correlation coefficient, r, then determine whether there is sufficient evidence to support the claim of a linear correlation between the two variables.
10
.632
.765
11
.602
.735
The linear correlation coefficient is r=
12
.576
.708
(Round to three decimal places as needed.)
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
.312
.402
45
.294
.378
50
.279
.361
60
.254
.330
70
.236
.305
.220
90
.207
.269
100
.196
256
NOTE: To test Ho:p = 0 against H: p + 0,
reject Ho if the absolute value of r is
greater than the critical value in the table.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F35b1a49f-318f-4190-9cbc-933b3a48d3d2%2F5f917622-89b3-4ec3-8b5b-d2fdc8c8b5fb%2Fj78mmnw_processed.png&w=3840&q=75)
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