The octane number, Y, of refined petroleum is related to the temperature, x, of therefining process. An experiment with sample size n = 11 gave a fitted least-squaresline ofwith V(1) (0.0193)².=ŷ = 4.265+0.190x,a. Give the test statistic you should use to test Ho: B₁ = 1,0 vs. Ha: ẞ₁ ẞ1,0 forsome fixed value ẞ1,0. Briefly explain your choice. [Hint: with the informationprovided, determine whether you should use a Z or at statistic.]b. Use your result from part (a) to test the hypothesis that the slope coefficient,ẞ1, is significantly different from 0 at significance level α = 0.05.

The linear regression equation is given as with Want to test The sample size is given as n=11to…

Answered: The octane number, Y, of refined…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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The heights (y) and lengths of forearms (x) were measured in inches for a sample of men. The following summary statistics were obtained: x= 10.1 Sx=0.8 y= 70.1 Sy=2.5 r=0.81 a. Compute the least- squares regresson line for predicting height from forearm length. b. Joe's forearm is 1 inch longer than Sam's. How much taller than Sam do you predict Joe to be? c. Predict the height of a man whose forearm is 9.5 inches long.
The Cadet is a popular model of sport utility vehicle, known for its relatively high resale value. The bivariate data given below were taken from a sample of fifteen Cadets, each bought new two years ago, and each sold used within the past month. For each Cadet in the sample, we have listed both the mileage x (in thousands of miles) that the Cadet had on its odometer at the time it was sold used and the price y (in thousands of dollars) at which the Cadet was sold used. The least-squares regression line for these data has equation y = 40.86-0.45x. This line is shown in the scatter plot below. Mileage, x (in thousands) 29.7 27.8 26.8 24.2 21.1 23.0 24.3 15.4 37.7 23.6 34.4 27.8 23.5 20.9 259 Used selling price, y (in thousands of dollars) 27.4 29.4 31.2 30.1 31.7 31.7 27.2 34.2 23.4 28.2 26.3 26.5 33.7 30.6 267 Used selling price (in thousands of dollars) 40- 35+ 30- 25- 20 THIS 15 X 20 X X X 30 Mileagex (in thousands) X 35 40
J In-shop othesis test for the difference between two population proportions 02562 2600368.qx3zqy7 Jump to level 1 The manager of a coffee shop is trying to determine if drive-through customers buy fewer items than customers who come into the shop. The manager randomly samples both populations and calculates the proportion of customers in each that buy three or more items. The results of the data collected are shown below. What are the population parameters? Y Pick Drive-through Successes 27 Successes What is the level of significance? Ex: 0.12 Observations 76 Observations 41 119 0.345 p-hat_1 0.355 p-hat_2 What is the null hypothesis Ho? Pick Confidence Level 0.1429 What is the alternative hypothesis Ha? Pick p-value Should Ho be rejected or does Ho fail to be rejected? Pick What conclusion can be drawn from the data? Pick evidence exists to support the claim that drive-through customers buy fewer items than in-shop customers. 2 p W
Suppose a doctor measures the height, x, and head circumference, y, of 8 children and obtains the data below. Thecorrelation coefficient is 0.944 and the least squares regression line is y = 0.199x + 11.982. Complete parts (a) and (b)below.Height, x27.5 25.5 26.25 25.25 27.5 26.25 26 27.25 27.25 27 27.25 ФHead Circumference, # 17.5 17.0 17.2 17.0 17.5 17.3 17.2 17.4 17.3 17.3 17.4(a) Compute the coefficient of determination, R?R?.% (Round to one decimal place as needed.)(b) Interpret the coefficient of determination and comment on the adequacy of the linear model.Approximately % of the variation inis explained by the least-squares regression model.According to the residual plot, the linear model appears to be (Round to one decimal place as needed.)
thill An experiment compares two different processes for producing steel plate. The measurements represent the thickness of the plate. The samples gave m = 8, X = 6.701, S1 = 0.108 n = 6, Y = 6.841, S2 = 0.155 %3D %3D Assume that the two populations are normal with equal variances, test Ho: H1 - H2 = 0 against H1 : µ1 - µ2#0 at a 0.05 significance level. 5.
16.17 In an experiment comparing four diets (treatments), the weight gain y (pounds per day) of pigs was recorded along with two covariates, initial age x₁ (days) and initial weight x2 (pounds). The data are presented in Table 16.11. (a) Using (16.67), (16.68), and (16.69), find Ex, exy, and eyy. Find B. (b) Using (16.77), (16.81), and (16.82), find SSEyr, SST.x, and SS(alu, B). Then test Ho: a₁ = ₂ = a3 = a4, adjusted for the covariates, using the F statistic in (16.83). (c) Test Ho: B = 0 using (16.84). (d) Find B₁, B₂, B3, and 4 using (16.88). Find SSE(F), and SSE(R)y.x using (16.86) and (16.87). Test Ho: B₁ B₂ B3 B4 using (16.89). X1 X2 y X1 78 61 1.40 78 90 59 1.79 99 94 76 1.72 80 71 50 1.47 75 1.26 94 1.28 91 1.34 75 1.55 63 1.57 62 1.26 TABLE 16.11 Initial Age x₁, Initial Weight x2, and Rate of Gain y of 40 Pigs Treatment 1. Treatment 2 Treatment 3 Treatment 4 99 61 80 54 83 57 75 45 62 41 67 40 X2 y X1 74 1.61 78 75 1.31 83 64 1.12 79 48 1.35 70 1.29 85 1.24 83 1.29 1.43 1.29…
You run a regression analysis on a bivariate set of data (n = 120). With i = 66.3 and y = 50.6, you obtain the regression equation y = 4.097x – 11.636 with a correlation coefficient of r = 0.56. You want to predict what value (on average) for the response variable will be obtained from a value of 120 as the explanatory variable. What is the predicted response value? y = (Report answer accurate to one decimal place.)
11. For temperature (x) and number of ice cream cones sold per hour (y). (65, 8), (70, 10), (75, 11), (80,13), (85, 12), (90, 16). Interpret the coefficient of determination. Optional Answers: 1. 88.2% of the variability in the number of cones sold is explained by the least-squares regression model. 2. 93.9% of the variability in the number of cones sold is explained by the least-squares regression model. 3. 88.2% of the variability in the temperature is explained by the least-squares regression model. 4. 93.9% of the variability in the temperature is explained by the least-squares regression model.
Given the following data set, let x be the explanatory variable and y be the response variable. x75 1 8812 y36102398 (a) If a least squares line was fitted to this data, what percentage of the variation in the y would be explained by the regression line? (Enter your answer as a percent.) ANSWER: % (b) Compute the correlation coefficient: r =
Q.4. In a study conducted to compare the yields of 4 treatments, the experimenter uses a plot with 4 rows and 4 columns. Which design is most likely to be used? Also, calculate the error, df.

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