random sample of 65 high school seniors was selected from all high school seniors at a certain high school. A scatterplot (not shown) revealed the height, in cm and foot length in cm, for each high school student from the sample. The association was described to be strong, positive, and linear. a. In the context of the study, explain what is meant by the following terms: positive: linear: b. The least squares regression equation was predicted height=105.08+2.599 (foot length). One of the students had a foot length of 20 cm. His residual was calculated to be 2.94 cm. What was the height of the student? c. suppose that the distribution of residuals is approximately normal with a standard deviation of 5.9 cm. What percent of residuals are less than 7 cm? Justify why.
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.
A random sample of 65 high school seniors was selected from all high school seniors at a certain high school. A scatterplot (not shown) revealed the height, in cm and foot length in cm, for each high school student from the sample. The association was described to be strong, positive, and linear.
a. In the context of the study, explain what is meant by the following terms:
positive:
linear:
b. The least squares regression equation was predicted height=105.08+2.599 (foot length). One of the students had a foot length of 20 cm. His residual was calculated to be 2.94 cm. What was the height of the student?
c. suppose that the distribution of residuals is approximately normal with a standard deviation of 5.9 cm. What percent of residuals are less than 7 cm? Justify why.
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