8 problem forest fires and acres burned an environmentalist...

Problem: 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 thousand's) of acres burned. The data for 8 recent years are shown. Fires x: 72 69 58 47 84 62 57 45 Acres y: 62 42 19 26 51 15 30 15 a. Draw the scatter plot for the variables. b. Compute the value of the correlation coefficient and identify the line of best fit (y' = a + bx) with the specific values for a and b from the problem below. c. Find y' when x = 60 fires. d. State the hypotheses. e. Test the significance of the correlation coefficient at α = 0.05. Using Table I or the P-value method. f. Give a brief explanation of the type of relationship. Assume all assumptions have been met.

Transcript

00:01 Hello student an environmentalist wants to determine the relation between number of forest fires over the years of cases of one year.

00:12 We have to calculate a correlation coefficient for the given data.

00:18 So from the given data first we calculate x bar, which is equal to six point 75.

00:24 Then we calculate y bar which is equal to 32 .5 and then we calculate summation of x i minus x bar square, which is equal to one one eight seven point five and summation of y i minus y bar square, which is equal to two one four six now summation of x i minus x bar into y i minus y bar which is equal to one two three zero now here formula for computing correlation coefficient is here r is equal to summation of x i minus x bar into y i minus y bar divided by square root of summation x i minus x bar square into y i minus y bar square.

01:30 Now here we substitute the values.

01:32 So here summation of x i minus x bar into y i minus y bar, which is equal to one two three zero divided by square root of one one eight seven point five into two one four six solving.

01:51 It will gives the value of correlation coefficient are therefore r is equal to zero point seventy seven.

02:00 Now here we have to find out a recreation equation here.

02:04 First we need to calculate the value of b1, which is calculated as summation of x i minus x bar into y i minus y bar divided by summation of x i minus x bar square here value of b1 is equal to one point zero three five.

02:29 Now here we have to calculate a value of b naught, which is calculated as y bar minus b1 x bar.

02:38 So here y bar is equal to thirty two point five minus b1 is equal to one point zero three five into x bar is equal to sixty one point seventy five.

02:54 Therefore value of b naught is equal to minus thirty one point forty six...

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