Forest Fires and Acres Burned An environmentalist wants to determine the relationships between the numbers (in thousands) of forest fires over the year and the number (in hundred thousands) of acres burned. The data for 7 recent years are shown. Number of fires x 47 84 62 57 45 72 69 Number of acres burned y 26 51 15 30 15 62 42 (a) Compute the value of the correlation coefficient. Round your answer to at least three decimal places. r= (b) State the hypotheses. H0 : H1: (c) Test the significance of the correlation coefficient at α=0.05 , using The Critical Values for the PPMC Table. Critical values: ± ▼(Choose one) the null hypothesis. (d) Give a brief explanation of the type of relationship. There ▼(Choose one) sufficient evidence to conclude that a significant linear relationship exists between the number of reported cases.
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.
Forest Fires and Acres Burned An environmentalist wants to determine the relationships between the numbers (in thousands) of forest fires over the year and the number (in hundred thousands) of acres burned. The data for 7 recent years are shown.
| Number of fires
x
|
47
|
84
|
62
|
57
|
45
|
72
|
69
|
|---|---|---|---|---|---|---|---|
| Number of acres burned
y
|
26
|
51
|
15
|
30
|
15
|
62
|
42
|
(a) Compute the value of the
r=
(b) State the hypotheses.
|
(c) Test the significance of the correlation coefficient at α=0.05 , using The Critical Values for the PPMC Table.
|
Critical values: ± ▼(Choose one) the null hypothesis. |
|
(d) Give a brief explanation of the type of relationship.
|
There ▼(Choose one) sufficient evidence to conclude that a significant linear relationship exists between the number of reported cases. |
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