A biological study of a minnow called the blacknose dace was conducted. The leng
ID: 3174156 • Letter: A
Question
A biological study of a minnow called the blacknose dace was conducted. The length, y (in millimeters), and the age, x (to the nearest year), were recorded.
x 1 1 3 2 4 1 1 1 3 4
y 90 82 87 75 50 67 66 82 84 79
(a) Draw a scatter diagram. (Do this on paper. Your instructor may ask you to turn in this work.)
(b) Calculate the correlation coefficient. (Give your answers correct to four decimal places.)
(c) Find the equation of the line of best fit. (Give your answers correct to two decimal places.)
y = + x
Consider this set of bivariate data.
x 2 1 3 4
y 2 2 1 2
(a) Draw a scatter diagram. (Do this on paper. Your instructor may ask you to turn in this work.)
(b) Calculate the correlation coefficient. (Give your answers correct to three decimal places.)
(c) Calculate the line of best fit. (Give your answers correct to two decimal places.)
y = + x
A study was conducted to investigate the relationship between the cost, y (in tens of thousands of dollars), per unit of equipment manufactured and the number of units produced per run, x. The resulting equation for the line of best fit is given below, with x being observed for values between 10 and 200. If a production run was scheduled to produce 65 units, what would you predict the cost per unit to be in dollars?
y = 7.26 0.08x
$
The values of x used to find points for graphing the line y = 14.8 + 0.61x are arbitrary. Suppose you choose to use x = 22 and x = 55.
(a) What are the corresponding y values? (Give your answers correct to one decimal place.)
y = (x = 22)
y = (x = 55)
Does it pay to study for an exam? The number of hours studied, x, is compared to the exam grade received, y.
x 5 7 1 6 4
y 75 70 75 95 70
(a) Find the equation for the line of best fit. (Round your answers to two decimal places.)
y = + x
The accompanying data show the number of hours, x, studied for an exam and the grade received, y (y is measured in tens; that is, y = 8 means that the grade, rounded to the nearest 10 points, is 80).
x
2
3
3
4
4
5
5
6
6
6
6
7
7
7
8
y
5
5
6
5
7
7
8
6
9
8
7
9
10
8
9
(a) Use the given scatter diagram to estimate r for the sample data on the number of hours studied and the exam grade.
r
(b) Calculate r. (Give your answer correct to two decimal places.)
r =
Does studying for an exam pay off? The number of hours studied, x, is compared with the exam grade received, y.
x 1 3 7 3 3
y 60 65 95 75 85
(a) Complete the preliminary calculations: SS(x), SS(y), and SS(xy).
(SS(x))
(SS(y))
(SS(xy))
(b) Find r. (Give your answer correct to three decimal places.)
x
2
3
3
4
4
5
5
6
6
6
6
7
7
7
8
y
5
5
6
5
7
7
8
6
9
8
7
9
10
8
9
Explanation / Answer
( a )
( b )
Correlation coefficient (r) = SS xy / [SS xx *SSyy ]
SS xx= sum of x^2 – (sum of x)^2 / n
SS yy = sum of y^ - (sum of y)^2 /n
SS xy = sum of xy – (sum of x * sum of y )/n
SS xx = 59 – (21*21)/10 = 14.9
SS yy = 59384 – (762*762)/10 = 1319.6
SS xy = 1566 – (21*762)/10 = -34.2
r = -34.2 / [14.9*1319.6] = -0.2439
The value of correlation is -0.2439
( c )
y^ = a + bx
b = SS xy / SS xx
= -34.2 / 14.9
= -2.2953
a = y bar – (b*x bar)
x bar = sum of x / n = 21/10 = 2.1
y bar = sum of y / n = 762/10 = 76.2
a = y bar – ( b * x bar ) = 76.2 – ( -2.2953*2.1) = 81.0201
y^ = 81.0201 -2.2953x
The line of regression is : y^ = 81.0201 -2.2953x
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