The manager of a hotel is considering expanding his hotel. Below are the mumber of nights the hotel was at least 95% booked during each of the last 7 years. Year Nights booked 1 2 3 21 16 24 28 32 34 39 Find the least squares regression equation that expresses the number of nights that are 95% booked each year as a linear function of time. Compute the forecasts for the years 8 and 9 using this model. Show all steps.
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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?Suppose Wesley is a marine biologist who is interested in the relationship between the age and the size of male Dungeness crabs. Wesley collects data on 1,000 crabs and uses the data to develop the following least-squares regression line where ? is the age of the crab in months and ?ˆ is the predicted value of ?, the size of the male crab in cm. ?ˆ=8.1312+0.5226? What is the value of ?ˆ when a male crab is 23.0736 months old? Provide your answer with precision to two decimal places. ?ˆ = Interpret the value of ?. The value of ?ˆis the predicted size of a crab when it is 23.0736 months old. the predicted incremental increase in size for every increase in age by 23.0736 months. the predicted number of crabs out of the 1,000 crabs collected that will be 23.0736 months old. the probability that a crab will be 23.0736 months old.Suppose Wesley is a marine biologist who is interested in the relationship between the age and the size of male Dungeness crabs. Wesley collects data on 1,000 crabs and uses the data to develop the following least-squares regression line where ? is the age of the crab in months and ?̂ is the predicted value of ?, the size of the male crab in cm. ?̂=8.2052+0.5693? What is the value of ?̂ when a male crab is 21.7865 months old? Provide your answer with precision to two decimal place
- Suppose the following data were collected from a sample of 5 car manufacturers relating monthly car sales to the number of dealerships and the quarter of the year. Use statistical software to find the following regression equation: SALESi= b0 + b1DEALERSHIPSi + b2 QUARTER1i+ b3QUARTER2i + b4QUARTER3i+ ei Is there enough evidence to support the claim that on average, car sales are higher in the 4th quarter than in the 2nd quarter at the 0.01 level of significance? If yes, write the regression equation in the spaces provided, rounded to two decimal places. Else, select "There is not enough evidence." Monthly Sales Number of Dealerships 1st Quarter (1 if Jan.-Mar., 0 otherwise) 2nd Quarter (1 if Apr.-Jun., 0 otherwise) 3rd Quarter (1 if Jul.-Sep., 0 otherwise) 4th Quarter (1 if Oct.-Dec., 0 otherwise) 85482 4 1 0 0 0 101319 9 1 0 0 0 121389 12 1 0 0 0 133677 18 1 0 0 0 194588 22 1 0 0 0 82128 4 0 1 0 0 150407 9 0 1 0 0 242714 12 0…The following information pertains to a simple least squares regression for DEF Corporation: Mean value of the dependent variable 30Mean value of the independent variable 8Coefficient of the independent variable 3Number of observations 12 What is the "a" value for the leasts-quares regression model? a. 60b. 30c. 6d. 0The following table shows the marks in statistics and economics for ten students. Fit a least square line to the data using a) ‘X’ as the independent variable b) What will be the regression equation if X= 20
- The following table shows the length, in centimeters, of the humerus and the total wingspan, in centimeters, of several pterosaurs, which are extinct flying reptiles. (A graphing calculator is recommended.) (a) Find the equation of the least-squares regression line for the data. (Where × is the independent variable.) Round constants to the nearest hundredth. y= ? (b) Use the equation from part (a) to determine, to the nearest centimeter, the projected wingspan of a pterosaur if its humerus is 52 centimeters. ? cmSuppose Wesley is a marine biologist who is interested in the relationship between the age and the size of male Dungeness crabs. Wesley collects data on 1,000 crabs and uses the data to develop the following least-squares regression line where ?X is the age of the crab in months and ?ˆY^ is the predicted value of ?Y, the size of the male crab in cm. ?ˆ=8.2052+0.5693?Y^=8.2052+0.5693X What is the value of ?ˆY^ when a male crab is 21.7865 months old? Provide your answer with precision to two decimal places. ?ˆ= Interpret the value of ?ˆ. The value of ?ˆ is the predicted number of crabs out of the 1,000 crabs collected that will be 21.7865 months old. the probability that a crab will be 21.7865 months old. the predicted size of a crab when it is 21.7865 months old. the predicted incremental increase in size for every increase in age by 21.7865 months.Suppose Wesley is a marine biologist who is interested in the relationship between the age and the size of male Dungeness crabs. Wesley collects data on 1,000 crabs and uses the data to develop the following least-squares regression line where ?X is the age of the crab in months and ?ˆY^ is the predicted value of ?Y, the size of the male crab in cm. ?ˆ=9.5603+0.3976?Y^=9.5603+0.3976X What is the value of ?ˆY^ when a male crab is 24.9118 months old? Provide your answer with precision to two decimal places. Y=
- The dean of the Business School at a small Florida college wishes to determine whether the grade-point average (GPA) of a graduate student can be used to predict the graduates starting salary. Records for 23 of last year’s Business School graduates were selected and the following least-squares regression line was calculated to predict starting salary (y) from GPA (x) and R2=.78. A) Circle the correct interpretation of R2.\ B) Suppose that you were one of the graduates in the study and the residual was negative. This means thatSuppose Wesley is a marine biologist who is interested in the relationship between the age and the size of male Dungeness crabs. Wesley collects data on 1,000 crabs and uses the data to develop the following least-squares regression line where ?X is the age of the crab in months and ?ˆY^ is the predicted value of ?Y, the size of the male crab in cm. ?ˆ=8.2052+0.5693? What is the value of ?^ when a male crab is 21.7865 months old? Provide your answer with precision to two decimal places. Y^ = Interpret the value of Y^.Following is information on the price per share and the dividend for asample of 30 companies.Company Price per Share Dividend1 $21.00 $ 3.342 23.12 3.56. . .. . .. . .39 81.90 18.5540 84.09 18.26Click here for the Excel Data FileRequired:a. Calculate the regression equation that predicts price per share basedon the annual dividend. (Round your answers to 4 decimal places.) b-1. State the null and alternate hypotheses.H0: β = 0 and H1: β ≠ 0H0: β = 0 and H1: β = 0H0: β ≠ 0 and H1: β ≠ 0H0: β ≤ 0 and H1: β > 0b-2. State the decision rule. Use the 0.05 significance level. (Round your answer to 3 decimal places )Price = 28.2064 + 2.4060 dividend b-2. State the decision rule. Use the 0.05 significance level. (Round your answer to 3 decimal places.) Reject H0 if t is not between ± 2.048 b-3. Compute the value of the test statistic. (Round your answer to 4 decimal places.) The test statistic is 7.3285b-4. What is your decision regarding…
