The following table gives the population in millions and the number of motor veh

Question

The following table gives the population in millions and the number of motor vehicle fatalities for 12 U. S. states in 2008 Explanatory Variable: Make a scatterplot of the data. Response variable: Write the line of best fit (the regression line), y cap = b_0 + b_1x. Find the Linear Correlation Coefficient and interpret: Find the Coefficient of Determination and interpret. Find the slope and interpret. Predict the value that you should expect for a state with a population of32.8 million and find the error for that prediction using the observations in the table above. Show your work.

Explanation / Answer

c.

Step 1: Find XY and X2 as it was done in the table below.

Step 2: Find the sum of every column:

X=502.8 , Y=312 , XY=18297.4 , X2=30722.78

Step 3: Use the following equations to find a and b:

a=YX2XXY/nX2(X)2=31230722.78502.818297.4/1230722.78502.823.328

b=nXYXY/nX2(X)2=1218297.4502.8312/1230722.78(502.8)20.541

Step 4: Substitute a and b in regression equation formula

y = a + bx=3.328+0.541x

d.

Step 1: Find XY , X2 and Y2 as it was done in the table below.

Step 2: Find the sum of every column to get:

X=502.8 , Y=312 , XY=18297.4 , X2=30722.78 , Y2=12056

Step 3: Use the following formula to work out the correlation coefficient.

r = nXYXY/sqrt[nX2(X)2][nY2(Y)2]= 1218297.4502.8312/sqrt[1230722.78502.82=

=0.8466

X Y XY XX 8.7 7 60.9 75.69 111.7 50 5585 12476.89 74.2 47 3487.4 5505.64 11.9 13 154.7 141.61 26.4 14 369.6 696.96 27 9 243 729 38.1 24 914.4 1451.61 44.9 19 853.1 2016.01 43.6 36 1569.6 1900.96 32.8 25 820 1075.84 65.9 63 4151.7 4342.81 17.6 5 88 309.76

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