otained for 20 randomly selected sets of siblings. The 20 pairs of measurements yield x = 99.21, y = 1 =presents the IQ score of the older child. Find the best predicted value of y given that the older child H the critical values of the Pearson correlation coefficient r. of ý is ces as needed.)
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.
![**Analysis of Sibling IQ Scores**
Suppose IQ scores were obtained for 20 randomly selected sets of siblings. The 20 pairs of measurements yield statistics as follows:
- Mean IQ score of older child (\( \bar{x} \)) = 99.21
- Mean IQ score of younger child (\( \bar{y} \)) = 101.2
- Pearson correlation coefficient (\( r \)) = 0.698
- P-value = 0.000
The regression equation used for prediction is:
\[ \hat{y} = 21.92 + 0.8x \]
where \( x \) represents the IQ score of the older child.
**Objective:** Find the best predicted value of \( \hat{y} \) given that the older child has an IQ of 92. A significance level of 0.05 is used for the analysis.
Instruction: Click the icon to view the critical values of the Pearson correlation coefficient \( r \).
**Best Predicted Value Calculation**
The best predicted value of \( \hat{y} \) is [input required].
*(Round to two decimal places as needed.)*](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8b154e39-9ebd-4de1-8fea-c901817b1837%2Fb41800e9-5730-4cca-9fe5-7be27d608145%2F4q7tcdp_processed.jpeg&w=3840&q=75)
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