Question

forest fires and acres burned numbers (in thousands) of forest fires over the year and the number (in hundred thousands) of acres years are shown.
number of fires x | 58 47 84 62 57 72 69
number of acres burned y | 54 43 80 58 53 68 65
send data to excel
the correlation coefficient for the data is r=1 and α=0.05. should regression analysis be done?
the regression analysis should not be done.
the regression analysis should be done.
find the equation of the regression line.
y=a+bx
a =
b =
find y when x=60.
y =

Explanation:

Step1: Check regression necessity

Since \( r = 1 \) (perfect positive correlation), regression is valid.

Step2: Calculate slope \( b \)

For perfect correlation, \( b = \frac{\text{change in } y}{\text{change in } x} = 1 \) (each \( y = x - 4 \)? No, wait: 58→54=58-4, 47→43=47-4, ..., 69→65=69-4. So \( y = x - 4 \), so \( b=1 \), \( a=-4 \)? Wait correction: 58-54=4, 47-43=4, ..., 69-65=4 → \( y = x - 4 \). So \( a=-4 \), \( b=1 \).

Step3: Find \( y' \) at \( x=60 \)

\( y' = -4 + 1×60 = 56 \)

Correction Step1: Verify perfect correlation

All \( y = x - 4 \), so \( r=1 \), regression should be done.

Step2: Regression equation

\( y' = -4 + x \) → \( a=-4 \), \( b=1 \)

Step3: Predict \( x=60 \)

\( y' = -4 + 60 = 56 \)

Final correction: The regression analysis should be done; \( a=-4 \), \( b=1 \); \( y'=56 \)

Step1: Determine regression validity

Perfect correlation (\( r=1 \)) → do regression.

Step2: Derive regression equation

All \( y = x - 4 \) → \( y' = x - 4 \).

Step3: Predict \( x=60 \)

\( y' = 60 - 4 = 56 \).

Answer:

The regression analysis should be done., a = 0, b = 1, y' = 60