2. A botanist is willing to understand the relation between volume, girth and height of black cherry trees. To this end, she collects data that is presented in trees table of the datasets library. Build a predictive multiple linear regression model for volume using girth and height as independent variables. a. What does the F-test tell about the model? Explain the result using the null hypothesis of the test. b. Provide confidence and prediction intervals for a black cherry tree with 10 inch of girth and 82 feet tall.
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- 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 researcher notes that, in a certain region, a disproportionate number of software millionaires were born around the year 1955. Is this a coincidence, or does birth year matter when gauging whether a software founder will besuccessful? The researcher investigated this question by analyzing the data shown in the accompanying table. Complete parts a through c below. a. Find the coefficient of determination for the simple linear regression model relating number (y) of software millionaire birthdays in a decade to total number (x) of births in the region. Interpret the result. The coefficient of determination is 1.___? (Round to three decimal places as needed.) This value indicates that 2.____ of the sample variation in the number of software millionaire birthdays is explained by the linear relationship with the total number of births in the region. (Round to one decimal place as needed.) b. Find the coefficient of determination for the simple linear regression model…A mail-order business selling personal computer supplies, software and hardware maintains a centralized warehouse. Management is currently examining the process of distribution from the warehouse and wants to study the factors that affect the warehouse distribution costs. Data collected over 24 random months contain the warehouse’s distribution cost (in thousands of Rands), the sales (in thousands of Rands) and the number of orders received. A multiple linear regression model was fitted to the data by using Stat1.2. Use the output to answer the questions that follow by typing only the letter of the correct option in the answer boxes. Variablesy: Warehouse Distribution Costx1: Salesx2: Number of Orders Model Fitting StatisticsR2 = 0.8504Adj R2: ? Regression Coefficients Beta Parameter Standard b Parameter Standard Estimates…
- Suppose that a kitchen cabinet warehouse company would like to be able to predict the area of a customer’s kitchen using the number of cabinets and the kitchen ceiling height. To do so data is collected on the following variables from a random sample of customers: Area – area of the kitchen in square feet Height – ceiling height in the kitchen (from floor to ceiling) in inches Cabinets – number of cabinets in the kitchen Suppose that a multiple linear regression model was fit to the data and that the following output resulted: Coefficients: (Intercept)HeightCabinets Estimate-57.98771.2760.3393 Std. Error8.63820.26430.1302 t value -6.7134.8282.607 Pr(>|t|)2.75e-074.44e-050.0145 What is the predicted area of a kitchen with a height of 96 inches and 10 cabinets? Report your answer to 1 decimal place. square feetSuppose that a kitchen cabinet warehouse company would like to be able to predict the area of a customer’s kitchen using the number of cabinets and the kitchen ceiling height. To do so data is collected on the following variables from a random sample of customers: Area – area of the kitchen in square feet Height – ceiling height in the kitchen (from floor to ceiling) in inches Cabinets – number of cabinets in the kitchen Suppose that a multiple linear regression model was fit to the data and that the following output resulted: Coefficients: (Intercept)HeightCabinets Estimate-57.98771.2760.3393 Std. Error8.63820.26430.1302 t value -6.7134.8282.607 Pr(>|t|)2.75e-074.44e-050.0145 10 Question 10 This is not a form; we suggest that you use the browse mode and read all parts of the question carefully. Which of the following is the correct interpretation of the coefficient for Cabinets? For a kitchen with a given ceiling height, the average number of cabinets…Suppose that a kitchen cabinet warehouse company would like to be able to predict the area of a customer’s kitchen using the number of cabinets and the kitchen ceiling height. To do so data is collected on the following variables from a random sample of customers: Area – area of the kitchen in square feet Height – ceiling height in the kitchen (from floor to ceiling) in inches Cabinets – number of cabinets in the kitchen Suppose that a multiple linear regression model was fit to the data and that the following output resulted: Coefficients: (Intercept)HeightCabinets Estimate-57.98771.2760.3393 Std. Error8.63820.26430.1302 t value -6.7134.8282.607 Pr(>|t|)2.75e-074.44e-050.0145 Why is the interpretation of the constant term (i.e. "intercept") not meaningful for this example? The predicted area will be negative when the number of cabinets is zero and the height of the kitchen is also zero. But we cannot have a negative area, nor a kitchen ceiling height of 0 inches.…
- Is there any multicollinearity problem in the above multiple regression model? How do you know? Risk of Stroke (%) Age Pressure Smoker (Yes=1) 12 57 152 0 24 67 163 0 13 58 155 0 56 86 177 1 28 59 196 0 51 76 189 0 18 56 155 1 31 78 120 0 37 80 135 1 15 78 98 0 22 71 152 0 36 70 173 1 15 67 135 1 48 77 209 0 15 60 199 0 36 82 119 1 8 66 166 0 34 80 125 1 3 62 117 0 37 59 207 1Consider the accompanying data on x = research and development expenditure (millions of dollars) and y = growth rate (% per year) for eight different industries. x 2.025 5.039 0.906 3.573 1.157 0.327 0.378 0.191 y 1.90 3.96 2.44 0.88 0.37 −0.90 0.49 1.01 (a) Would a simple linear regression model provide useful information for predicting growth rate from research and development expenditure? Test the appropriate hypotheses using a 0.05 significance level. Calculate the test statistic. (Round your answer to two decimal places.) t = Use technology to find the P-value for this test. (Round your answer to four decimal places.) P-value = What can you conclude? Reject H0. We have convincing evidence of a useful linear relationship between growth rate and research and development expenditure.Fail to reject H0. We have convincing evidence of a useful linear relationship between growth rate and research and development expenditure. Fail to reject H0. We do not have…Consider the accompanying data on x = research and development expenditure (millions of dollars) and y = growth rate (% per year) for eight different industries. x 2.025 5.037 0.906 3.573 1.157 0.327 0.378 0.191 y 1.90 3.96 2.44 0.88 0.37 −0.90 0.49 1.01 (a) Would a simple linear regression model provide useful information for predicting growth rate from research and development expenditure? Test the appropriate hypotheses using a 0.05 significance level. Calculate the test statistic. (Round your answer to two decimal places.) t = Use technology to find the P-value for this test. (Round your answer to four decimal places.) P-value = What can you conclude? Reject H0. We have convincing evidence of a useful linear relationship between growth rate and research and development expenditure. Fail to reject H0. We have convincing evidence of a useful linear relationship between growth rate and research and development expenditure. Fail to reject H0. We do not have…
- In the packaging department of a large aircraft parts distributor, a fairly reliable estimate of packaging and processing costs can be determined by knowing the weight of an order. Thus, the weight is a cost driver that accounts for a sizable fraction of the packaging and processing costs at this company. Data for the past 10 orders are given as follows. Solve, a. Estimate the b0 and b1 coefficients, and determine the linear regression equation to fit these data. b. What is the correlation coefficient (R)? c. If an order weighs 250 lb, how much should it cost to package and process it?According to "Reproductive Biology of the Aquatic Salamander Amphiuma tridactylum in Louisiana,"† the size of a female salamander's snout is correlated with the number of eggs in her clutch. The following data are consistent with summary quantities reported in the article. Partial Minitab output is also included. Snout-Vent Length Clutch Size 32 45 53 215 53 160 53 170 54 190 57 200 57 270 58 175 58 245 59 215 63 170 63 240 64 245 67 280 The regression equation is Y = -133 + 5.92x Predictor Coef Stdev T P Constant -133.02 64.30 2.07 0.0608 x 5.919 1.127 5.25 0.0002 s = 33.90 R-sq = 69.7% R-sq(adj) = 67.2% Additional summary statistics are given below. n = 14 x = 56.5 y = 201.4 Σx2 = 45,597 Σy2 = 613,550 Σxy = 164,690 You can use the Distribution Calculators page in SALT to find critical values and/or p-values to answer parts of this question. (a) What is the equation of the regression line…The height (in feet) and trunk circumference (in inches) at breast height (4.5 feet above the ground)was measured for a random sample of Eucalyptus trees. The data are summarized below.Trunk Circumference 21.1 20.8 22.5 19.4 23.6 19.8 21.6 19.9Tree Height 34.2 32.7 35.0 31.9 36.5 31.2 33.8 31.4(a) Determine the linear regression model that will best predict the height of a Eucalyptus treebased on its trunk circumference at breast height.
