Let x = day of observation and y = number of locusts per square meter during a locust infestation in a region of North Africa. x 2 3 5 8 10 y 2 3 12 125 630 (a) Draw a scatter diagram of the (x, y) data pairs. Do you think a straight line will be a good fit to these data? Do the y values almost seem to explode as time goes on? No. A straight line does not fit the data well. The data seem to explode as x increases.Yes.
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.
Let x = day of observation and y = number of locusts per square meter during a locust infestation in a region of North Africa.
| x | 2 | 3 | 5 | 8 | 10 |
| y | 2 | 3 | 12 | 125 | 630 |
(b) Now consider a transformation y' = log (y). We are using common logarithms of base 10. Draw a scatter diagram of the (x, y') data pairs and compare this diagram with the diagram of part (a). Which graph appears to better fit a straight line?
(c) Use a calculator with regression keys to find the linear regression equation for the data pairs (x, y'). What is the
| y' = | + x |
| r = |
(d) The exponential growth model is y = αβx. Estimate α and β and write the exponential growth equation. (Use 4 decimal places.)
| α = | |
| β = | |
| = | · x |
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