An article in the journal of pharmaceutical sciences (80, 971-977, 1991) presents data on the observed mole fraction solubility of a solute at a constant temperature, along with x1 = dispersion partial solubility, x2 = dipolar partial solubility, and x3 = hydrogen bonding hansen partial solubility. the response y is the negative logarithm of the mole fraction solubility.
(a) fit a complete second order model to the data.
(b) test for the overall significance of the regression.
(c) examine the residual plots and comment on the model adequacy.
(d) report r2 and r2adj. which gives a better assessment of the models predictive ability?
(e) test whether the second order terms are significant to the regression.
y x1 x2 x3
0.222 7.3 0 0
0.395 8.7 0 0.3
0.422 8.8 0.7 1
0.437 8.1 4 0.2
0.428 9 0.5 1
0.467 8.7 1.5 2.8
0.444 9.3 2.1 1
0.378 7.6 5.1 3.4
0.494 10 0 0.3
0.456 8.4 3.7 4.1
0.452 9.3 3.6 2
0.112 7.7 2.8 7.1
0.432 9.8 4.2 2
0.101 7.3 2.5 6.8
0.232 8.5 2 6.6
0.306 9.5 2.5 5
0.0923 7.4 2.8 7.8
0.116 7.8 2.8 7.7
0.0764 7.7 3 8
0.439 10.3 1.7 4.2
0.0944 7.8 3.3 8.5
0.117 7.1 3.9 6.6
0.0726 7.7 4.3 9.5
0.0412 7.4 6 10.9
0.251 7.3 2 5.2
0.2 7.6 7.8 20.7

region b will make the inequalities y < 2x + 1 and y > -x - 2 true ⇒ answer a

step-by-step explanation:

* lets study the graph and the inequality to solve the question

- the inequality y > -x - 2

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = -2 that means the line intersect the y-axis at point (0 , -2)

∵ the sign of the inequality is >

∴ we shad the part over the line

  region a and b

- the inequality y < 2x + 1

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = 1 that means the line intersect the y-axis at point (0 , 1)

∵ the sign of the inequality is <

∴ we shad the part under the line

  region b and c

∵ the common region between the two lines is region b

∴ region b will make the inequalities y < 2x + 1 and y > -x - 2 true

this is a direct variation proportion. y = kx

y is the total amount due, k is the constant of variation, and x is the number of texts sent.

plug in the 3.20 and the 16 to solve for the "k". this is the constant of proportionality. it is the value that will not change.

3.20 = k(16). solving you get $.20 per text.

the equation would then be y = .20x