The number of motor vehicles registered in millions in the US has grown as follows:

Year: 1940, 1945 1950, 1955, 1960, 1965, 1970, 1975, 1980, 1985

Vehicles: 32.4, 31.0, 49.2, 62.7, 73.9, 90.4, 108.4, 132.9, 155.8, 171.7

(Where Year = X and Vehicles = Y)

Use logarithms to transform the data into a linear association. White the equation of the LSRL. Your answer should have logs in it. Remember to define any variables.

a. Present a scatter plot for the data. (Hint: let x = 0 represent the year 1940)

b. Determine the correlation coefficient for the data and interpret the value.

a) Figure attached

b)  

For our case we have this:

n=10  

So then the correlation coefficient would be r =0.989

Step-by-step explanation:

Previous concepts

The correlation coefficient is a "statistical measure that calculates the strength of the relationship between the relative movements of two variables". It's denoted by r and its always between -1 and 1.

Solution to the problem

Part a

Year (x): 1940, 1945 1950, 1955, 1960, 1965, 1970, 1975, 1980, 1985

Vehicles (Y): 32.4, 31.0, 49.2, 62.7, 73.9, 90.4, 108.4, 132.9, 155.8, 171.7

After apply natural log for the two variables and create the scatterplot in excel we got the following result on the figure attached.

Part b

And in order to calculate the correlation coefficient we can use this formula:  

For our case we have this:

n=10  

So then the correlation coefficient would be r =0.989

x = -4

step-by-step explanation:

- 20 - 4(x + 3) = 4x

=> -20 - 4x - 12 = 4x

=> - 32 -4x = 4x

=> -32 = 4x + 4x

=> - 32 = 8x

=> -32/8 = x

=> -4 = x