Height, x IQ score, y 61 108 58 105 64 106 68 113 58 96 63 110 66 119 56 129 the table of critical values for the Pearson correlation coefficient. n alpha=0.05 alpha=0.01 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 21 0.433 0.549 22 0.423 0.537 23 0.413 0.526 24 0.404 0.515 25 0.396 0.505 26 0.388 0.496 27 0.381 0.487 28 0.374 0.479 29 0.367 0.471 30 0.361 0.463 35 0.334 0.430 40 0.312 0.403 45 0.294 0.380 50 0.279 0.361 55 0.266 0.345 60 0.254 0.330 65 0.244 0.317 70 0.235 0.306 75 0.227 0.296 80 0.220 0.286 85 0.213 0.278 90 0.207 0.270 95 0.202 0.263 100 0.197 0.256 ----------------------------------------------------------------------------------- (a) Display the data in a scatter plot. (b) Calculate the sample correlation coefficient r. r=_______________________ (Round to three decimal places as needed.) (c) Describe the type of correlation, if any, and interpret the correlation in the context of the data. There is__________linear correlation. Interpret the correlation. Choose the correct answer below. A .As high school girls' heights increase, their IQ scores tend to increase. B. Based on the correlation, there does not appear to be any relationship between high school girls' heights and their IQ scores. C. As high school girls' heights increase, their IQ scores tend to decrease. D. Increases in high school girls' heights cause their IQ scores to decrease. E. Based on the correlation, there does not appear to be a linear relationship between high school girls' heights and their IQ scores. F. Increases in high school girls' heights cause their IQ scores to increase. (d) Use the table of critical values for the Pearson correlation coefficient to make a conclusion about the correlation coefficient. Let α=0.01. The critical value is_________ (Round to three decimal places) Therefore, there is ( is or is not) ________sufficient evidence at the 1% level of significance to conclude that_________________ (there is significant correlation or there is no correlation) between high school girls' heights and their IQ scores.
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.
61 108
58 105
64 106
68 113
58 96
63 110
66 119
56 129
the table of critical values for the Pearson correlation coefficient.
n alpha=0.05 alpha=0.01
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
21 0.433 0.549
22 0.423 0.537
23 0.413 0.526
24 0.404 0.515
25 0.396 0.505
26 0.388 0.496
27 0.381 0.487
28 0.374 0.479
29 0.367 0.471
30 0.361 0.463
35 0.334 0.430
40 0.312 0.403
45 0.294 0.380
50 0.279 0.361
55 0.266 0.345
60 0.254 0.330
65 0.244 0.317
70 0.235 0.306
75 0.227 0.296
80 0.220 0.286
85 0.213 0.278
90 0.207 0.270
95 0.202 0.263
100 0.197 0.256
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(a) Display the data in a
(b) Calculate the sample correlation coefficient r.
r=_______________________
(Round to three decimal places as needed.)
(c) Describe the type of correlation, if any, and interpret the correlation in the context of the data.
There is__________linear correlation.
Interpret the correlation. Choose the correct answer below.
A .As high school girls' heights increase, their IQ scores tend to increase.
B. Based on the correlation, there does not appear to be any relationship between high school girls' heights and their IQ scores.
C. As high school girls' heights increase, their IQ scores tend to decrease.
D. Increases in high school girls' heights cause their IQ scores to decrease.
E. Based on the correlation, there does not appear to be a linear relationship between high school girls' heights and their IQ scores.
F. Increases in high school girls' heights cause their IQ scores to increase.
(d) Use the table of critical values for the Pearson correlation coefficient to make a conclusion about the correlation coefficient. Let α=0.01.
The critical value is_________ (Round to three decimal places)
Therefore, there is ( is or is not) ________sufficient evidence at the
1% level of significance to conclude that_________________ (there is significant correlation or there is no correlation)
between high school girls' heights and their IQ scores.
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