A random sample of 65 high school seniors was selected from all high school seniors at a certain high school. The following scatterplot shows the height, in centimeters (cm), and the foot length, in cm, for each high school senior from the sample. The least-squares regression line is shown. The computer output from the least-squares regression analysis is also shown. Term Coef (SE) Coef T-Value P-Value Constant 105.08 6.00 17.51 0.000 Foot length 2.599 0.238 10.92 0.000 S=5.90181 R–sq=65.42% (a) Calculate and interpret the residual for the high school senior with a foot length of 20cm and a height of 160cm. (b) The standard deviation of the residuals is s=5.9. Interpret the value in context. (c) The following histogram summarizes the 65 residuals. Assume that the distribution of residuals is approximately normal with mean 0cm and standard deviation 5.9cm. What percent of the residuals are greater than 8cm? Justify your answer. (d) Based on your answer to part (c), would it be surprising to randomly select a high school senior from the high school with a foot length of 20cm and a height greater than 165cm? Justify your answer.
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. The following
| Term | Coef | (SE) Coef | T-Value | P-Value |
| Constant | 105.08 | 6.00 | 17.51 | 0.000 |
| Foot length | 2.599 | 0.238 | 10.92 | 0.000 |
| S=5.90181 | R–sq=65.42% |
(a) Calculate and interpret the residual for the high school senior with a foot length of 20cm and a height of 160cm.
(b) The standard deviation of the residuals is s=5.9. Interpret the value in context.
(c) The following histogram summarizes the 65 residuals.
Assume that the distribution of residuals is approximately normal with mean 0cm and standard deviation 5.9cm. What percent of the residuals are greater than 8cm? Justify your answer.
(d) Based on your answer to part (c), would it be surprising to randomly select a high school senior from the high school with a foot length of 20cm and a height greater than 165cm? Justify your answer.
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