Question

4. ix small Oregon cities give the following information about x and y values:

    per capita income in thousands(x)   8.6       9.3       10.1     8.0       8.3 8.7                                          
    number of medical doctors(y)         9.6       18.5     20.9     10.2     11.4     13.1
   
a) Make a scatterplot. Label your axes and the scales used.
b) What is the linear correlation coefficient?
c) Compute the equation of the least squares regression line.
d) What percent of the relationship between x and y is explained by a line?
    e) Graph the least squares regression line on your scatterplot. Identify the points used.
    f) If the per capita income was $10,800 predict the number of medical doctors.
    g) What is the residual for (10.1, 20.9)? Round to the nearest tenth.

Answer 1

Here in this Question we have the Smll regon cities give the following information about x Income per capita income in thousands(x) number of medical doctors(y).

Based on given Sample we considered the x thousands is independent variable X and numbers of medical doctors Y is dependent variable.

Here we used the simple linear regression because here the one independent variable. If we have significant correlation then we can used the simple linear regression model on given sample.

First,

Also, the following calculations are needed to compute the correlation coefficient:

	X	Y	X*Y	X2	Y2
	8.6	9.6	82.56	73.96	92.16
	9.3	18.5	172.05	86.49	342.25
	10.1	20.9	211.09	102.01	436.81
	8.0	10.2	81.6	64	104.04
	8.3	11.4	94.62	68.89	129.96
	8.7	13.1	113.97	75.69	171.61
Sum =	53	83.7	755.89	471.04	1276.83

Now,

The Question a) to c) the scatter plot, correlation coefficient and regression equation is calculated using following formula and steps,

Now,

d) there is strong positive relationships between the income in thousands x and number of doctors Y.

The value of correlation coefficient is r= 0.934 then the coefficient of determination r^2= 0.87.2.

Which means there is 87.2% variation in y medical doctors Variable explained by x regressor variable.

f) The predicted number of medical doctors whos income is $10,800 is ,

Yhat = -36.898 + 5.7564*10.8

Yhat = 25.2

The predicted numbers of medical doctors whos income is $ 10,800 is 25 doctors.

This is first four answer of your sub Questions .

Thank you.