Concept explainers
Suppose
a. Interpret the regression coefficient associated with variable
b. Interpret the regression coefficient associated with variable
c. Suppose that the
Want to see the full answer?
Check out a sample textbook solutionChapter 14 Solutions
EP BASIC BUS.STATS-ACCESS (18 WEEKS)
- Find the equation of the regression line for the following data set. x 1 2 3 y 0 3 4arrow_forwardRespiratory Rate Researchers have found that the 95 th percentile the value at which 95% of the data are at or below for respiratory rates in breath per minute during the first 3 years of infancy are given by y=101.82411-0.0125995x+0.00013401x2 for awake infants and y=101.72858-0.0139928x+0.00017646x2 for sleeping infants, where x is the age in months. Source: Pediatrics. a. What is the domain for each function? b. For each respiratory rate, is the rate decreasing or increasing over the first 3 years of life? Hint: Is the graph of the quadratic in the exponent opening upward or downward? Where is the vertex? c. Verify your answer to part b using a graphing calculator. d. For a 1- year-old infant in the 95 th percentile, how much higher is the walking respiratory rate then the sleeping respiratory rate? e. f.arrow_forwardOlympic 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?arrow_forward
- 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?arrow_forwardA trucking company considered a multiple regression model for relating the dependent variable y = total daily travel time for one of its drivers (hours) to the predictors x₁ = distance traveled (miles) and x₂ = the number of deliveries made. Suppose that the model equation is Y = -0.800+ 0.060x₁ +0.900x₂ + e (a) What is the mean value of travel time when distance traveled is 50 miles and four deliveries are made? hr (b) How would you interpret ₁ = 0.060, the coefficient of the predictor x₁? O When the number of deliveries is constant, the average change in travel time associated with a ten-mile (i.e. one unit) increase in distance traveled is 0.060 hours. O The total daily travel time increases by 0.060 hours when the distance traveled increases by 1. O When the number of deliveries is held fixed, the average change in travel time associated with a one-mile (i.e. one unit) increase in distance traveled is 0.060 hours. O The average change in travel time associated with a one-mile (i.e.…arrow_forwardSuppose that a regional express delivery service company wants to estimate the cost of shipping a package (Y) as a function of cargo type, where cargo type includes the following possibilities: fragile, semi-fragile, and durable. Costs for 15 randomly chosen packages of approximately the same weight and same distance shipped, but of different cargo types, are provided in the file P14_16.xlsx. a. Estimate a regression equation using the given sample data, and interpret the estimated regression coefficients. b. According to the estimated regression equation, which cargo type is the most costly to ship? Which cargo type is the least costly to ship? c. How well does the estimated equation fit the given sample data? How might the fit be improved? d. Given the estimated regression equation, predict the cost of shipping a package with semi-fragile cargo.arrow_forward
- A company specializing in home decoration items would like to build a regression model consisting of 5 factors to predict sales. Data for the past 24 months on sales and 5 factors were collected for one particular home decoration item and the SPSS package was used to get the output. The relevant outputs are given below in Tables 1 and 2. The variables for which the data has been collected are as follows Dependent variable Y = monthly sales in lakhs (for one particular home decoration item) Independent variables 1)advertising cost in lakhs 2)competition index 3)number of existing customers 4) number of dealer outlets 5) number of personnel delivering to the customer The company decided to follow Stepwise Multiple Linear Regression. Read the output data given below and answer the questions given Table 1 Multiple R 0.965 R square 0.931 Adjusted R square 0.895 Standard Error 4.235 From the ANOVA table, the extracted P value is 0.001 Table 2…arrow_forwardA 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. Using data collected for a sample ofn 91 houses in East Meadow, the appraiser fit the data with the following simple, linear regression model: y = 91.80 + 19.72, where x = number of rooms and y = appraised value of the house (in thousands of dollars). Additionally, the appraiser determined the coefficient of correlation to be r = .93 and the coefficient of determination to be r %3D = .86. Give a practical interpretation of the coefficient of correlation. B IUS Ix E三 三 三 E E E Insert Formula IIarrow_forwardHow to compute for the 1. ∑x2 2. ∑ y2 3. ∑xy of this data set for linear regression?arrow_forward
- Identify two different conditions under which the regression line should not be used to make predictions.arrow_forwardIf the linear correlation coefficient between the explanatory variable (x) and response variable (y) is r = 0.73, the slope of the regression line is negative O not enought information to answer O positivearrow_forwardA software firm collected data for a sample of 30 computer programmers. A regression analysis can be used to determine if annual salary ($1000s) was related to the years of experience, the score on the firm's programmer aptitude test, and gender. Question: To test the joint significance of the two factors, test score and gender, in Model 1, given a = 5%, the conclusion of the test is Model 1: Standard Intercept experience Test score female Coefficients Error 9.3536 1.4888 0.1851 -2.3613 SST-599.7855, SSE= 75.9380 6.2008 0.1829 0.0757 1.0607 Filters Add a caption.. > +919773521433arrow_forward
- Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw HillTrigonometry (MindTap Course List)TrigonometryISBN:9781305652224Author:Charles P. McKeague, Mark D. TurnerPublisher:Cengage Learning
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageCollege AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningFunctions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning