Question

Six 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 scenario it is given that the Six small Oregon cities give the following information about per capita income.

Here we have to use simple linear regression model. Based on given sample.

The independent variable is XX, and the dependent variable is YY. In order to compute the regression coefficients, the following table needs to be used:

	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

Based on the above table, the following is calculated:

Now,

a) a scatterplot is given in above steps.

b) there is a strong positive linear correlation coefficient bet x thousands and y medical doctor. Because of the Correlation coefficient value is positive 0.934.

c) the equation of the least squares regression line is,

Yhat = -36.898 + 5.7564X.

d) the relationship between x and y is explained by a line:

The relationship between x and y is strong positive relationships.

Now the r^2 = 0.872. which means there is 87.2% variation in y Variable explained by x independent variable.

e) Graph of the least squares regression line on scatterplot is given above.

f) the per capita income was $10,800 the predicted number of medical doctors is,

Yhat = -36.898 + 5.7564*10.8

Yhat = 25.27.

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

This is the first 6 answer of your Question.

Thank you.