Question

The following table shows the annual number of PhD graduates in a country in various fields.

	Natural Sciences	Engineering	Social Sciences	Education
1990	70	10	60	30
1995	130	40	120	50
2000	330	130	280	120
2005	490	370	460	210
2010	590	550	830	520
2012	690	590	1,000	900

(a)

With x = the number of social science doctorates and y = the number of education doctorates, use technology to obtain the regression equation. (Round coefficients to three significant digits.)

y(x) =

Graph the associated points and regression line.

(b)

What does the slope tell you about the relationship between the number of social science doctorates and the number of education doctorates?

The slope tells us the increase in the number of social science doctorates for each additional education doctorate.The slope tells us the decrease in the number of social science doctorates for each additional education doctorate.    The slope tells us the decrease in the number of education doctorates for each additional social science doctorate.The slope tells us the increase in the number of education doctorates for each additional social science doctorate.

(c)

Use technology to obtain the coefficient of correlation r. (Round your answer to three decimal places.)

r =

Does the value of r suggest a strong correlation between x and y?

Since r is close to 0, the correlation between x and y is a strong one.Since r is close to 0, the correlation between x and y is a weak one.    Since r is close to 1, the correlation between x and y is a weak one.Since r is close to 1, the correlation between x and y is a strong one.

(d)

Does the graph suggest a roughly linear relationship between x and y? Why or why not?

No, the graph suggests a concave-down curve rather than a straight line.Yes, the graph suggests a straight line.    Yes, the graph suggests a concave-down curve rather than a straight line.Yes, the graph suggests a concave-up curve rather than a straight line.No, the graph suggests a concave-up curve rather than a straight line.

Answer 1

Ans:

a)

Last option is correct.

education, y 1000 200 400 600 800 1000 1200

b)The slope tells us the increase in the number of education doctorates for each additional social science doctorate.

c) coefficient of correlation r=0.962

d)

.No, the graph suggests a concave-up curve rather than a straight line.