An article in Wood Science and Technology, "Creep in Chipboard, Part 3: Initial Assessment of the Influence of Moisture Content and Level of Stressing on Rate of Creep and Time to Failure" (1981, Vol. 15, pp. 125-144) studied the deflection (mm) of particleboard from stress levels of relative humidity. Assume that the two variables are related according to the simple linear regression model. The data are shown below 54 54 61 61 x = Stress level (%) y = Deflection (mm) 16.473 18.693 14.305 15.121 13.505 11.64 11.168 12.534 11.224 68 68 75 75
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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?The following fictitious table shows kryptonite price, in dollar per gram, t years after 2006. t= Years since 2006 0 1 2 3 4 5 6 7 8 9 10 K= Price 56 51 50 55 58 52 45 43 44 48 51 Make a quartic model of these data. Round the regression parameters to two decimal places.The table presents data on the taste test of 38 brands of pinot noir wine [data were first reported in an article by Kwan, Kowalski, and Skogenboe in the Journal Agricultural and Food Chemistry (1979, Vol. 27), the response variable is y = quality, and we want to find the "best" regression equation that relates quality to the other five parameters
- The monthly premium quoted by an insurance company for a critical illness policy was collected from a sample of 6 adult male smokers at different age. The data for the sample are shown: Age 28 25 50 39 47 31 Premium ($) 75 40 175 125 250 105 Using Age to predict premium, the Linear Regression equation is given by: ŷ =6.556X−112 and r2=0.813y^=6.556X−112 and r2=0.813 a. Identify the independent and Dependent variables. Dependent: Age Premium Independent: Age Premium b. Determine the slope. Slope = Slope = Round to 3 decimal places c. Determine |r||r| . |r|=|r|= Round to 3 decimal places d. Interpret rr : and e. Determine critical r value at 5% significance level and determine if there is a significant linear correlation exists. |r| critical=|r| critical= Round to 3 decimal places Linear Correlation:Linear Correlation: Significant Not Significant f. Predict the monthly premium for a 40 years old adult male smoker.…The Update to the Task Force Report on Blood Pressure Control in Children [12] reported the observed 90th per-centile of SBP in single years of age from age 1 to 17 based on prior studies. The data for boys of average height are given in Table 11.18. Suppose we seek a more efficient way to display the data and choose linear regression to accomplish this task. age sbp 1 99 2 102 3 105 4 107 5 108 6 110 7 111 8 112 9 114 10 115 11 117 12 120 13 122 14 125 15 127 16 130 17 132 Do you think the linear regression provides a good fit to the data? Why or why not? Use residual analysis to justify your answer. Am I supposed to run a residual plot and QQ-plot for this question?It is believed that the annual repair cost for the sporty automobile Jeep is related to its age. A sample of 11 automobiles revealed the results in the table at the right. Car age (xi) 2 3 1 7 5 8 1 2 6 9 4 Repair cost (yi) in £ 72 99 65 138 67 140 83 101 170 121 114 Define the terms regression and correlation analysis . From the simple linear model ,y= a + bx ,determine parameters a and b
- It is believed that the annual repair cost for the sporty automobile Jeep is related to its age. A sample of 11 automobiles revealed the results in the table at the right. Car age (xi) 2 3 1 7 5 8 1 2 6 9 4 Repair cost (yi) in £ 72 99 65 138 67 140 83 101 170 121 114 Define the terms regression and correlation analysis From the simple linear model , determine parameters and , with an interpretation of your linear model What would be the cost of repairing car that has been in use for 13 yearsThe 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.An article in Wear (Vol. 152, 1992, pp 171-181) presents data on the fretting wear of mild steel and oil viscosity. Representative data follow, with x = oil viscosity and y = wear volume (10-4 mm3) : 1. Determine the coefficient of determination. 2. Test the significance of the correlation coefficient. 3. Find the simple linear regression model. 4. Predict fretting wear when viscosity is 30. Construct a prediction interval for the estimate. 5. Do you think Simple Linear Regression is the best relationship to use for this data? Test for Linear Transforms and come up with a conclusion.
- Life insurance companies are keenly interested in predicting how long their customers are likely to live, because this will determine their premiums and ultimately their profitability. An Australian life insurance company is interested in the relationship, if any, between the age at death of their male customers and that of the customer’s father. Data are collected on a random sample of 100 of their male customers who have recently died. The customer’s age at death was plotted against that of their father and a linear regression model applied. Relevant output is shown below. Say how you know from the output that there actually is a significant linear relationship between a male customer’s age at death and his father’s age at death. State the value of the coefficient of Father’s Age (Death) and interpret this value in the context of the problem at hand.State the value of the coefficient of determination in the model and interpret this value in the context of the situation.Life insurance companies are keenly interested in predicting how long their customers are likely to live, because this will determine their premiums and ultimately their profitability. An Australian life insurance company is interested in the relationship, if any, between the age at death of their male customers and that of the customer’s father. Data are collected on a random sample of 100 of their male customers who have recently died. The customer’s age at death was plotted against that of their father and a linear regression model applied. Relevant output is shown below Examine both the scatterplot and the correlation matrix provided above. Comment on the apparent relationship between the customer’s age at death and their father’s age at death in the plot. Explain how the information in the correlation matrix supports your conclusionIf the general linear regression model is given by the equation: y = a + b?; considering the informationobtained in Figure 2 above, compute the value of a.