Heights (cm) and weights (kg) are measured for 100 randomly selected adult males, and range from heights of 139 to 193 cm and weights of 40 to 150 kg. Let the predictor variable x be the first variable given. The 100 paired measurements yield x= 167.40 cm, y= 81.42 kg, r=0. 119, P-value 0.238, and y = - 101+1.09x. Find E the best predicted value of y (weight) given an adult male who is 156 cm tall. Use a 0.05 significance level. The best predicted value of y for an adult male who is 156 cm tall is (Round to two decimal places as needed.) kg.
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.
![**Study of Height and Weight Correlation in Adult Males**
In a research conducted with a sample of 100 randomly selected adult males, the heights (in centimeters) and weights (in kilograms) were measured. The height range found among the participants was from 139 cm to 193 cm, while the weight range spanned from 40 kg to 150 kg.
The study aimed to explore the correlation between height and weight, with height set as the predictor variable (\(x\)). From the 100 paired observations, the data analysis yielded the following results:
- Mean height (\(\overline{x}\)): 167.40 cm
- Mean weight (\(\overline{y}\)): 81.42 kg
- Correlation coefficient (\(r\)): 0.119
- P-value: 0.238
- Linear regression equation: \(\hat{y} = -101 + 1.09x\)
The objective is to find the best predicted weight for an adult male whose height is 156 cm, using a significance level of 0.05.
The formula for the predicted weight (\(\hat{y}\)) is applied as follows:
\[ \hat{y} = -101 + 1.09 \times 156 \]
After calculating using the formula, the predicted weight for a male who is 156 cm tall is:
\[ \hat{y} = -101 + 169.64 = 68.64 \text{ kg} \]
Thus, the best predicted value of weight for an adult male with a height of 156 cm is **68.64 kg**, rounded to two decimal places.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff9d7df7e-1211-4d2e-80e0-69c049749f41%2F3d9f4e14-3ed5-44ac-89ca-270fbff84965%2Fcoe88z.jpeg&w=3840&q=75)
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