Refer back to the data in Exercise 4, in which y = ammo- nium concentration (mg/L) and x transpiration (ml/h). Summary quantities include n = 13, Ex, = 303.7, Ey, = 52.8, S = 1585.230769, S,, = -341.959231, and S, = %3D %3D yy 77.270769. a. Obtain the equation of the estimated regression line and use it to calculate a point prediction of ammo- nium concentration for a future observation made when ammonium concentration is 25 ml/h. b. What happens if the estimated regression line is used to calculate a point estimate of true average concentration when transpiration is 45 ml/h? Why does it not make sense to calculate this point estimate? c. Calculate and interpret s. d. Do you think the simple linear regression model does a good job of explaining observed variation in con- centration? Explain.

Refer back to the data in Exercise 4, in which y = ammo- nium concentration (mg/L) and x transpiration (ml/h). Summary quantities include n = 13, Ex, = 303.7, Ey, = 52.8, S = 1585.230769, S,, = -341.959231, and S, = %3D %3D yy 77.270769. a. Obtain the equation of the estimated regression line and use it to calculate a point prediction of ammo- nium concentration for a future observation made when ammonium concentration is 25 ml/h. b. What happens if the estimated regression line is used to calculate a point estimate of true average concentration when transpiration is 45 ml/h? Why does it not make sense to calculate this point estimate? c. Calculate and interpret s. d. Do you think the simple linear regression model does a good job of explaining observed variation in con- centration? Explain.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter7: Analytic Trigonometry

Section7.6: The Inverse Trigonometric Functions

Problem 91E

See similar textbooks

Similar questions

The table below shows the number of state-registered automatic weapons and the murder rate for several Northwestern states. xx 11.9 8.3 6.9 3.9 2.7 2.4 2.1 0.7 yy 14.3 11.3 10 7.4 6.5 6.4 5.9 4.9 xx = thousands of automatic weaponsyy = murders per 100,000 residentsThis data can be modeled by the equation y=0.84x+4.23. Use this equation to answer the following;Special Note: I suggest you verify this equation by performing linear regression on your calculator.Use the equation with the values rounded to two decimal places to make your predictions.A) How many murders per 100,000 residents can be expected in a state with 5.5 thousand automatic weapons?Answer = Round to 3 decimal places.B) How many murders per 100,000 residents can be expected in a state with 3.9 thousand automatic weapons?Answer = Round to 3 decimal places.
The table below shows the number of state-registered automatic weapons and the murder rate for several Northwestern states. xx 11.9 8.6 6.8 3.8 2.6 2.7 2.5 0.5 yy 14 11.5 9.6 7.2 5.9 6.5 6.3 4.6 xx = thousands of automatic weaponsyy = murders per 100,000 residentsThis data can be modeled by the equation y=0.84x+4.08. Use this equation to answer the following;Special Note: I suggest you verify this equation by performing linear regression on your calculator.A) How many murders per 100,000 residents can be expected in a state with 7.8 thousand automatic weapons?Answer = Round to 3 decimal places.B) How many murders per 100,000 residents can be expected in a state with 1.5 thousand automatic weapons?Answer = Round to 3 decimal places.
The data given below indicate the existence of a linear relationship between the x and y variables. Suppose an analyst who prepared the solutions and carried out the RI measurements was not skilled and as a result of poor technique, allowed intermediate errors to appear. The results are the following:Concentration of solution in percent (x) 10 26 33 50 61Refractive indices (y) 1.497 1.493 1.485 1.478 1.477Step 1. Carefully plot the given x and y values (from the table) on a regular graphing paper. Label then connect the points to observe a zigzag plot due to the scattered points. Step 2: Copy and fill the table given below: x (x - x̄) (x - x̄) 2 y (y - ȳ) (y - ȳ) 2 (x - x̄) (y - ȳ) 10 1.497 26 1.49333 1.48550 1.47861 1.477∑ = ∑ = ∑ = ∑ = ∑ = ∑ = ∑ =x̄= ∑xi ÷ Nx̄= ȳ = ∑yi ÷ Nȳ = Step 3. After completing the table, present following computations and the interpretation.a. Calculate the correlation coefficient (r), using the working formula: r =Σ (x − x ) (y − ȳ)√(Σ(x − x )2)(Σ(y −…
Consider the following data relating hours spent studying (X) and average grade on course quizzes (Y): X Y 5 6 3 8 4 8 7 10 5 7 6 9 Compute SP (equation below) Consider the following data relating hours spent studying (X) and average grade on course quizzes (Y): X…
The analysis of tooth shrinkage by C. Loring Brace and colleagues at the University of Michigan’s Museum of Anthropology indicates that human tooth size is con-tinuing to decrease and that the evolutionary process has not yet come to a halt. In northern Europeans, for example, tooth size reduction now has a rate of 1% per 1000 years. a. If t represents time in years and y represents tooth size, use the condition that y = 0.99y0 when t = 1000 to find the value of k in the equation y = y0 ekt. Then use this value of k to answer the following questions. b. In about how many years will human teeth be 90% of their present size? c. What will be our descendants’ tooth size 20,000 years from now (as a percentage of our present tooth size)?
Do you think E(y)=β0+β1 ln⁡|x|+ β2ex+β3x3 is a linear statistical model What about E(y)=β0+β1x1+eβ2x2 ?
Determine the best (according to sum-of-squares-measure) curve y = Aebx , through the data above. Transformed equation ln(y) = ln(A) + bx or Y = a + bx.
You study the relation between the log excess return on stock XYZ, denoted by Re XY Z,t, and the log excess return on the market portfolio, Re M,t, based on 193 monthly observations: R e XY Z,t = β1 + β2 R e M,t + uXY Z,t. You run this regression in R and obtain from the standard regression output the following parameter estimates and p-values (in squared brackets): Re XY Z,t = −0.3199 + 2.0262 Re M,t + uXY Z,t. [0.7689] [0.0001] (1) (a) Which econometric conclusions you can draw from the p-value of the intercept coefficient? In your answer, clearly explain the meaning of the p-value. Further, refer to the role of the significance level in the context of the test of significance approach, i.e., which steps of the test are (not) affected
Given are five observations for two variables, x and y. xi 1 2 3 4 5 yi 4 6 5 9 14 Develop the estimated regression equation by computing the the slope and the y intercept of the estimated regression line (to 1 decimal). y^= + x Use the estimated regression equation to predict the value of y when x = 5 (to 1 decimal).y^ =
An investigation into the relationship between an adolescent mother's age x in years and the birth weight y of her baby in grams yielded the regression equation y= - 1163.45 + 245.15x as well as r = .88369, r2= .78091, SSE = 337212.45, and s= 205.30844 1) What is the predicted birth weight for a baby brn to a 17 year old woman? 2) What is the propotion of the variability in the weights of babies born to adolescent mothers that is accounted for by the mother's age? 3) For every additional year in the mother's age that mean birth weight of the baby? (a) increases by about 245g (b) decreases by about 245g (c) increases by about 1163g (d) increases by about 1163g (e) changes by an amount that cannot be determined from the information given.
In a regression analysis involving 30 observations, the following estimated regression equation was obtained. ŷ = 16.7 + 3.5x1 − 2.3x2 + 7.9x3 + 2.9x4 (a)Interpret b1 in this estimated regression equation. -b1 = 7.9 is an estimate of the change in y corresponding to a 1 unit change in x3 when x1, x2, and x4 are held constant. -b1 = 2.9 is an estimate of the change in y corresponding to a 1 unit change in x4 when x1, x2, and x3 are held constant. -b1 = 3.5 is an estimate of the change in y corresponding to a 1 unit change in x1 when x2, x3, and x4 are held constant. -b1 = 3.5 is an estimate of the change in y corresponding to a 1 unit change in x2 when x1, x3, and x4 are held constant. -b1 = −2.3 is an estimate of the change in y corresponding to a 1 unit change in x1 when x2, x3, and x4 are held constant.Interpret b2 in this estimated regression equation. -b2 = −2.3 is an estimate of the change in y corresponding to a 1 unit change in x1 when x2, x3, and x4 are held…
At Chairs and More, assemblers are apud according to the following differential piece rate scale 1-25 chairs in a week, $10 each; 26-40 chairs in a week $13 each; 40 up chairs in a week $17.50. Salina Grant assembled 47 chairs in one week. Find her gross pay.