Water is being poured into a large, cone-shaped cistern. The volume of water, measured in cm, is reported at different time intervals, measured in seconds. A regression analysis was completed and is displayed in the computer output. What is the equation of the least-squares regression line? Volume = 0.640 - 0.006(Time) Regression Analysis: cuberoot (Volume) versus Time O Volume = 0.640 - 0.006(Time) Fredictor Coef SE Coef Constant -0.006 0.00017 -35.294 0.000 Volume = -0.006 + 0.640(Time) tima n640 n000018 355126

Water is being poured into a large, cone-shaped cistern. The volume of water, measured in cm, is reported at different time intervals, measured in seconds. A regression analysis was completed and is displayed in the computer output. What is the equation of the least-squares regression line? Volume = 0.640 - 0.006(Time) Regression Analysis: cuberoot (Volume) versus Time O Volume = 0.640 - 0.006(Time) Fredictor Coef SE Coef Constant -0.006 0.00017 -35.294 0.000 Volume = -0.006 + 0.640(Time) tima n640 n000018 355126

Trigonometry (MindTap Course List)

8th Edition

ISBN:9781305652224

Author:Charles P. McKeague, Mark D. Turner

Publisher:Charles P. McKeague, Mark D. Turner

Chapter4: Graphing And Inverse Functions

Section: Chapter Questions

Problem 6GP: If your graphing calculator is capable of computing a least-squares sinusoidal regression model, use...

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If your graphing calculator is capable of computing a least-squares sinusoidal regression model, use it to find a second model for the data. Graph this new equation along with your first model. How do they compare?
Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s pole vault height has fallen below the value predicted by the regression line in Example 2. This might have occurred because when the pole vault was a new event there was much room for improvement in vaulters’ performances, whereas now even the best training can produce only incremental advances. Let’s see whether concentrating on more recent results gives a better predictor of future records. (a) Use the data in Table 2 (page 176) to complete the table of winning pole vault heights shown in the margin. (Note that we are using x=0 to correspond to the year 1972, where this restricted data set begins.) (b) Find the regression line for the data in part ‚(a). (c) Plot the data and the regression line on the same axes. Does the regression line seem to provide a good model for the data? (d) What does the regression line predict as the winning pole vault height for the 2012 Olympics? Compare this predicted value to the actual 2012 winning height of 5.97 m, as described on page 177. Has this new regression line provided a better prediction than the line in Example 2?
A county real estate appraiser wants to develop a statistical model to predict the appraised value of houses in a section of the county called East Meadow. One of the many variables thought to be an important predictor of appraised value is the number of rooms in the house. Consequently, the appraiser decided to fit the simple linear regression model: E(y) = β0 + β1x, where y = appraised value of the house (in thousands of dollars) and x = number of rooms. Using data collected for a sample of n = 74 houses in East Meadow, the following results were obtained: = 74.80 + 19.84 xGive a practical interpretation of the estimate of the slope of the least squares line. For a house with 0 rooms, we estimate the appraised value to be $74,800. For each additional room in the house, we estimate the appraised value to increase $74,800. For each additional room in the house, we estimate the appraised value to increase $19,840. For each additional dollar of…
The first step of the Durbin-Watson test for the presence of autocorrelation is to estimate the model and determine Select one: a. the residuals lagged one period. b. the current period residuals and the residuals lagged one period. c. the current period residuals. d. the current period residuals, the residuals lagged one period, and the residuals lagged two periods.
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Please solve the attached parts a,b, and c and provide final answers rounded as needed in each part Table of temperatures versus sugar: Linear regression equation: ŷ = 6.3318 + 1.8818x Temperature, x Converted Sugar, y 1 8.2 1.1 7.9 1.2 8.7 1.3 9.7 1.4 9.3 1.5 8.6 1.6 8.5 1.7 10.5 1.8 9.2 1.9 9.5 2 10.6
Compute the least-squares regression equation for the given data set. Use a TI-84 calculator. Round the slope and y intercept to at least four decimal places. x 5 7 6 2 1 y 4 3 2 5 1 Regression line equation: =
The Tiliche Corp. analyst conducted 10 independent timing studies in the manual spray painting section of the finishing department. The product line under study revealed a direct relationship between spray painting time and product surface area. The following data were collected (ignore the qualification factor): (image) a) Find the linear model relating standard time (y) to surface area (x) using linear regression.(x) using linear regression.b) How much time would you allocate to spray painting a new part with a surface area of 250 in2?surface area of 250 in2?c) Obtain the fitted value of y and the corresponding residual for a particular assembly (study #3), with a surface area of 250 inches2?(study #3), with an area of 150 square inches.d) Perform a significance test of the regression using α= 0.05. Find the P-value for this test.What are your conclusions?e) Estimate the standard errors of the slope and the value of the intercept.f) Calculate the coefficient of determination R2 .g)…
The owner of Showtime Movie Theaters, Inc., would like to predict weekly gross revenueas a function of advertising expenditures. Historical data for a sample of eight weeks follow. Weekly GrossRevenue($1000s) Television Advertising($1000s) Newspaper Advertising($1000s) 96 5.0 1.5 90 2.0 2.0 95 4.0 1.5 92 2.5 2.5 95 3.0 3.3 94 3.5 2.3 94 2.5 4.2 94 3.0 2.5 a. Develop an estimated regression equation with the amount of televisionadvertising as the independent variable.b. Develop an estimated regression equation with both television advertising and newspaper advertising as the independent variables. c. Is the estimated regression equation coefficient for television advertisingexpenditures the same in part (a) and in part (b)? Interpret the coefficient in each case. d. Predict weekly gross revenue for a week when $3500 is spent on television advertising and $1800 is spent on newspaper advertising.
The measure of standard error can also be applied to the parameter estimates resulting from linear regressions. For example, consider the following linear regression equation that describes the relationship between education and wage: WAGEi=β0+β1EDUCi+εi where WAGEi is the hourly wage of person i (i.e., any specific person) and EDUCi is the number of years of education for that same person. The residual εi encompasses other factors that influence wage, and is assumed to be uncorrelated with education and have a mean of zero. Suppose that after collecting a cross-sectional data set, you run an OLS regression to obtain the following parameter estimates: WAGEi=−11.5+6.1 EDUCi If the standard error of the estimate of β1 is 1.32, then the true value of β1 lies between(4.78, 4.12, 3.46, 5.44) and (6.76, 7.42, 8.74) . As the number of observations in a data set grows, you would expect this range to (DECREASE , INCREASE) in size.
Suppose that researchers are interested in determining the bi-annual salary of statisticians of different levels using their years of experience and their education level (M = bachelors, P = doctorate). They fit the following model to a dataset that includes these variables and, after performing the proper steps of multiple linear regression, the following multiple linear regression model is obtained: yˆ = 42308 + 323x1 + 213x2 + 301(x1*x2) where the variables are as follows: yˆ = predicted bi−annual salary in dollars, x1 = number of years of experiencex2= {1 if the education level is a doctorate 0 if the education level is a bachelors What is the predicted bi-annual salary in dollars of an employee with 5 years of experience and a bachelor’s degree?
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