Suppose IQ scores were obtained for 20 randomly selected sets of couples. The 20 pairs of measurements yield x = 100.08, y = 99.15, r = 0.899, P-value =0.000, and y=−5.36+1.04x, where x represents the IQ score of the wife. Find the best predicted value of y given that the wife has an IQ of 98? Use a significance level of 0.05. Critical Values of the Pearson Correlation Coefficient r n α =0.05 α =0.01 NOTE: To test H0: ρ =0 against H1: ρ ≠0, reject H0 if the absolute value of r is greater than the critical value in the table. 4 0.950 0.990 5 0.878 0.959 6 0.811 0.917 7 0.754 0.875 8 0.707 0.834 9 0.666 0.798 10 0.632 0.765 11 0.602 0.735 12 0.576 0.708 13 0.553 0.684 14 0.532 0.661 15 0.514 0.641 16 0.497 0.623 17 0.482 0.606 18 0.468 0.590 19 0.456 0.575 20 0.444 0.561 25 0.396 0.505 30 0.361 0.463 35 0.335 0.430 40 0.312 0.402 45 0.294 0.378 50 0.279 0.361 60 0.254 0.330 70 0.236 0.305 80 0.220 0.286 90 0.207 0.269 100 0.196 0.256 n α =0.05 α =0.01
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.
Suppose IQ scores were obtained for 20 randomly selected sets of couples. The 20 pairs of measurements yield
x
=
100.08,
y
=
99.15, r
=
0.899, P-value
=0.000, and
y=−5.36+1.04x, where x represents the IQ score of the
wife. Find the best predicted value of
y given that the
wife has an IQ of
98? Use a significance level of 0.05.
Critical Values of the Pearson
|
n |
α
=0.05 |
α
=0.01 |
NOTE: To test H0:
ρ
=0 against H1:
ρ
≠0, reject H0 if the absolute value of r is greater than the critical value in the table. |
|
4 |
0.950 |
0.990 |
|
|
5 |
0.878 |
0.959 |
|
|
6 |
0.811 |
0.917 |
|
|
7 |
0.754 |
0.875 |
|
|
8 |
0.707 |
0.834 |
|
|
9 |
0.666 |
0.798 |
|
|
10 |
0.632 |
0.765 |
|
|
11 |
0.602 |
0.735 |
|
|
12 |
0.576 |
0.708 |
|
|
13 |
0.553 |
0.684 |
|
|
14 |
0.532 |
0.661 |
|
|
15 |
0.514 |
0.641 |
|
|
16 |
0.497 |
0.623 |
|
|
17 |
0.482 |
0.606 |
|
|
18 |
0.468 |
0.590 |
|
|
19 |
0.456 |
0.575 |
|
|
20 |
0.444 |
0.561 |
|
|
25 |
0.396 |
0.505 |
|
|
30 |
0.361 |
0.463 |
|
|
35 |
0.335 |
0.430 |
|
|
40 |
0.312 |
0.402 |
|
|
45 |
0.294 |
0.378 |
|
|
50 |
0.279 |
0.361 |
|
|
60 |
0.254 |
0.330 |
|
|
70 |
0.236 |
0.305 |
|
|
80 |
0.220 |
0.286 |
|
|
90 |
0.207 |
0.269 |
|
|
100 |
0.196 |
0.256 |
|
|
n |
α
=0.05 |
α
=0.01 |
|
Step by step
Solved in 3 steps with 2 images
