The following data are the morning and evening high tide levels for Charleston, SC from January 1-14,2017. The information for the PM high tide for January 4 is missing. Create a scatter plot. Find the regression line and use it to estimate the PM high tide for January 4. Then find the correlation coefficient. (NOTE: The first column identifies the day. This data will not be used in the scatter plot.)
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.
The following data are the morning and evening high tide levels for Charleston, SC from January 1-14,2017. The information for the PM high tide for January 4 is missing. Create a
| Day | AM High (in feet), x |
|---|
| PM High (in feet), y |
|---|
| 1 | 5.6 | 4.8 |
| 2 | 5.5 | 4.8 |
| 3 | 5.4 | 4.9 |
| 4 | 5.2 | |
| 5 | 5.0 | 5.1 |
| 6 | 5.2 | 5.0 |
| 7 | 5.4 | 4.9 |
| 8 | 5.7 | 5.0 |
| 9 | 6.0 | 5.1 |
| 10 | 6.3 | 5.3 |
| 11 | 6.4 | 5.4 |
| 12 | 6.5 | 5.4 |
| 13 | 6.4 | 5.4 |
| 14 | 6.2 | 5.3 |
Source: SCDHEC.gov
1. What is the response variable? (morning high tide levels/ evening high tide levels)
2. What is the regression line equation? (Round each value to the nearest hundredth, if necessary.) y = ___________ + or - _______________x
3. We can expect the PM high tide on January 4 to be approximately ________ feet. (Round to the nearest tenth, if necessary.) This is an example of _____________ (extrapolation/ interpolation)
4. The correlation coefficient is _______________. This value means that there is ________________ (no/weak/moderate/strong). A _____________ correlation between the AM and PM tide levels. (no/positive/negative)
5. Change the regression model from linear to test and see if an exponential or a quadratic
6. Use the new equation to estimate the value of the PM high time on January 4. The estimated PM high tide is ______________ (Round to the nearest tenth, if necessary.)
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