Feature recognition from surface models of complicated parts is becoming increasingly important in the development of efficient computer-aided design (CAD) systems. The article “A Computationally Efficient Approach to Feature Abstraction In Design-Manufacturing Integration" (J. of Engr. for Industry, 1995: 16-27) contained a graph of log10( total recognition time), with time in sec. versus log10 number of edges of a part), from which the following representative values were read:
Log(edges) | 1.1 | 1.5 | 1.7 | 1.9 | 2.0 | 2.1 |
Log(time) | .30 | .50 | .55 | .52 | .85 | .98 |
Log( edges) | 2.2 | 2.3 | 2.7 | 2.8 | 3.0 | 3.3 |
Log(time) | 1.10 | 1.00 | 1.18 | 1.45 | 1.65 | 1.84 |
Log(edges) | 3.5 | 3.8 | 4.2 | 4.3 | ||
Log(time) | 2.05 | 2.46 | 2.50 | 2.76 |
- a. Does a
scatterplot of log(time) versus log(edges) suggest an approximate linear relationship between these two variables? - b. What probabilistic model for relating y = recognition time to x = number of edges is implied by the simple linear regression relationship between the transformed variables?
- c. Summary quantities calculated from the data are
n = 16
Calculate estimates of the parameters for the model in part (b). and then obtain a point prediction of time when the number of edges is 300.
Want to see the full answer?
Check out a sample textbook solutionChapter 13 Solutions
Probability and Statistics for Engineering and the Sciences
- What does the y -intercept on the graph of a logistic equation correspond to for a population modeled by that equation?arrow_forwardA deficiency of the trace element selenium in the diet can negatively impact growth, immunity, muscle and neuromuscular function, and fertility. The introduction of selenium supplements to dairy cows is justified when pastures have low selenium levels. Authors of the article “Effects of Short-Term Supplementation with Selenised Yeast on Milk Production and Composition of Lactating Cows” (Australian J. of Dairy Tech., 2004: 199–203) supplied the following data on milk selenium concentration (mg/L) for a sample of cows given a selenium supplement and a control sample given no supplement, both initially and after a 9-day period. Obs Init Se Init Cont Final Se Final Cont 1 11.4 9.1 138.3 9.3 2 9.6 8.7 104 8.8 3 10.1 9.7 96.4 8.8 4 8.5 10.8 89 10.1 5 10.3 10.9 88 9.6 6 10.6 10.6 103.8 8.6 7 11.8 10.1 147.3 10.4 8 9.8 12.3 97.1 12.4 9 10.9 8.8 172.6 9.3 10 10.3…arrow_forwardInfants, even newborns, prefer to look at attractive faces compared to less attractive faces (Slater, et al., 1998). In the study, infants from 1 to 6 days old were shown two photographs of women’s faces. Previously, a group of adults had rated one of the faces as significantly more attractive than the other. The babies were positioned in front of a screen on which the photographs were presented. The pair of faces remained on the screen until the baby accumulated a total of 20 seconds of looking at one or the other. The number of seconds looking at the attractive face was recorded for each infant. Suppose that the study used a sample of n = 9 infants and the data produced an average of M = 13 for the attractive face with an estimated standard error sM= 1 (SS = 72). If there were no preference, the 20 seconds should be divided equally between the two photographs. Note that all the available information comes from the sample. Specifically, we do not know the population mean or the…arrow_forward
- Infants, even newborns, prefer to look at attractive faces compared to less attractive faces (Slater, et al., 1998). In the study, infants from 1 to 6 days old were shown two photographs of women’s faces. Previously, a group of adults had rated one of the faces as significantly more attractive than the other. The babies were positioned in front of a screen on which the photographs were presented. The pair of faces remained on the screen until the baby accumulated a total of 20 seconds of looking at one or the other. The number of seconds looking at the attractive face was recorded for each infant. Suppose that the study used a sample of n = 9 infants and the data produced an average of M = 13 for the attractive face with an estimated standard error sM= 1 (SS = 72). If there were no preference, the 20 seconds should be divided equally between the two photographs. Note that all the available information comes from the sample. Specifically, we do not know the population mean or the…arrow_forwardSuppose the table below displays the estimation results from the Logit model Regressor Coefficient (standard error) (log)Income(X1) 0.48 (0.12) Age(X2) 0.03 (0.01) -0.008 (0.02) constant 8.07 (1.16) where the heteroskedasticity-robust standard errors are reported along with the coefficient estimates. How do you interpret the coefficient on log income? Is it significantly different from zero? What is the log odds-ratio for an individual with log income equal to 10 and age equal to 40? Explain what it means.arrow_forwardThe total number of thousands of tons of coal produced per year over a 10-year period for a certain region is provided in the accompanying dataset. Use double exponential smoothing to determine which pairs of values for α and β minimize MAD for this dataset. α=0.2, β=0.9; α=0.4, β=0.2; α=1, β=0.7 Year Coal Production (thousands of tons)1 434,3272 420,4213 439,0394 477,1985 504,1796 526,9577 546,8208 564,8839 556,70210 570,984 First find the MAD for each pair of values, α and β. (Type integers or decimals rounded to two decimal places as needed.) α β MAD 0.2 0.9 nothing 0.4 0.2 nothing 1 0.7 nothingarrow_forward
- Here is a dataset containing plant growth measurements of plants grown in solutions of commonly-found chemicals in roadway runoff.Phragmites australis, a fast-growing non-native grass common to roadsides and disturbed wetlands of Tidewater Virginia, was grown in a greenhouse and watered with either: Distilled water (control); A weak petroleum solution (representing standard roadway runoff); Sodium chloride solution; Magnesium chloride solution; De-icing brine (50% sodium chloride and 50% magnesium chloride).Twenty grass preparations were used for each solution, and total growth (in cm) was recorded after watering every other day for 40 days.-Perform the correct statistical test to determine the p-value.-Report your answer rounded to four decimal places.-You should use formulas, functions, and the Data Analysis ToolPak in MS Excel to avoid additive rounding errors. Here are some useful functions: =t.test(array1,array2,tails,type) Produces a p-value for any…arrow_forwardThe owner of a moving company typically has his most experienced manager predict the total number of labor hours that will be required to complete an upcoming move. This approach has proved useful in the past, but the owner has the business objective of developing a more accurate method of predicting labor hours. In a preliminary effort to provide a more accurate method, the owner has decided to use the number of cubic feet moved as the independentvariable and has collected data for 36 moves in which the origin and destination were within the borough of Manhattan in New York City and in which the travel time was an insignificant portionof the hours worked. The intercept for the sample regression line that the owner has computed is -2.37 and the slope is 0.04. If the actual number of labor hours for moving 407 cubic feet is 33.47. What is the error of prediction? Hint: Provide answer accurate to 2 decimal places.arrow_forwardThe total number of thousands of tons of coal produced per year over a 10-year period for a certain region is provided in the accompanying dataset. Use double exponential smoothing to determine which pairs of values for α and β minimize MAD for this dataset. α=0.2, β=0.8; α=0.4, β=0.2; α=0.9, β=0.7 First find the MAD for each pair of values, α and β.arrow_forward
- Smitley and Davis studied the changes in gypsy moth egg mass density over one generation as a function of the initial egg mass density in a control plot and two treated plots. The data below are for the control plot. Initial Egg Mass (per 0.04 ha) 50 75 100 160 175 180 200 Change in Egg Mass Density (%) 250 -100 -25 -25 -50 50 0 A. On the basis of the data given in the table, find the best-fitting logarithmic function using least squares. State the square of the correlation coefficient. (Note that the authors used logarithms to the base 10.) (Use 4 decimal places in your answers.)y(x) = r2 = B. Use this model to estimate the change in egg mass density with an initial egg mass of 120 per 0.04 ha. (Use 4 decimal places in your answer.)With an initial egg mass of 120 per 0.04ha, the change in mass density is %arrow_forwardWhat is the critical value from the t-table?arrow_forwardCompute the forecasted values for Yt for July and August in 2020 by using the modelsstated in (c) and (d)arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage