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PLEASE HELP WITH PART B) at the bottom, I keep getting incorrect. WILL THUMBS UP IF CORRECT.
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- The following table provides values of the function f(x,y). However, because of potential; errors in measurement, the functional values may be slightly inaccurately. Using the statistical package included with a graphical calculator or spreadsheet and critical thinking skills, find the function f(x,y)=a+bx+cy that best estimate the table where a, b and c are integers. Hint: Do a linear regression on each column with the value of y fixed and then use these four regression equations to determine the coefficient c. x y 0 1 2 3 0 4.02 7.04 9.98 13.00 1 6.01 9.06 11.98 14.96 2 7.99 10.95 14.02 17.09 3 9.99 13.01 16.01 19.02Respiratory 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.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 data is representative of that reported in the article "An Experimental Correlation of Oxides of Nitrogen Emissions from Power Boilers Based on Field Data,"t with x = burner-area liberation rate (MBtu/hr-ft2) and NO, emission rate (ppm). 100 125 125 150 150 200 200 250 250 300 300 350 400 400 150 140 180 210 190 320 280 400 430 440 390 600 610 670 The equation of the estimated regression line is y = -45.55190539 + 1.71143233x. (a) Obtain SSE for the data from the defining formula SSE = (Y; - ŷ;)<|. (Round your answer to two decimal places.) Compare to the value calculated from the computational formula. (When comparing, round your value from the computational formula to two decimal places.) Rounded to two decimal places the value from the computational formula is ---Select--- v the defining formula. (b) Calculate the value of total sum of squares. (Round your answer to two decimal places.) Does the simple linear regression model appear to do an effective job of explaining…A researcher records age in years (x) and systolic blood pressure (y) for volunteers. They perform a regression analysis was performed, and a portion of the computer output is as follows: ŷ = 4.3 14.9x Coefficients (Intercept) X Estimate St 4.3 Ho: B₁ = 0 Ha: B₁ > 0 B1 O Ho: B₁ Ha: B₁ <0 = 0 14.9 B1 O Ho: B₁ = 0 0 Ha: B1 Std. Error Test statistic P-value 2.9 5.1 1.48 Specify the null and the alternative hypotheses that you would use in order to test whether a negative linear relationship exists between x and y. 2.92 0.08 0.01A researcher records age in years (x) and systolic blood pressure (y) for volunteers. They perform a regression analysis was performed, and a portion of the computer output is as follows: ŷ = 3.3 +12.7x Coefficients (Intercept) X Estimate Std. Error Test statistic O Ho: B₁: = 0 Ha: B₁ 0 O Ho: B₁ = 0 Ha: B₁ 0 12.7 2.2 6.4 1.5 1.98 P-value Specify the null and the alternative hypotheses that you would use in order to test whether a positive linear relationship exists between x and y. 0.08 0.03
- A researcher records age in years (x) and systolic blood pressure (y) for volunteers. They perform a regression analysis was performed, and a portion of the computer output is as follows: ŷ = 4.5+ 14.4x Coefficients (Intercept) x Estimate 4.5 Ho: B₁ = 0 H₁: B₁ > 0 Ho: B₁ = 0 Ha: B₁ <0 14.4 Ho: B₁ = 0 Ha: B₁ #0 Std. Error Test statistic 2.9 4.7 1.55 3.06 P-value Specify the null and the alternative hypotheses that you would use in order to test whether a linear relationship exists between x and y. 0.07 0The quality of the orange juice produced by a certain manufacturer is constantly monitored. Data collected on the sweetness index of an orange juice sample and amount of water-soluble pectin for 24 production runs at a juice manufacturing plant are shown in the accompanying table. Suppose a manufacturer wants to use simple linear regression to predict the sweetness (y) from the amount of pectin (x). Find and interpret the coefficient of determination, r2, and the coefficient of correlation, r. Find and interpret the coefficient of determination, r2. Select the correct choice below and fill in the answer box within your choice. (Round to three decimal places as needed.) A. The coefficient of determination, r2, is enter your response here. Sample variations in the amount of water-soluble pectin explain 100r2% of the sample variation in the sweetness index using the least squares line. B. The coefficient of determination, r2, is enter your…The data below is for a hypothetical study investigating the Systolic Blood Pressure (SBP) of construction workers. The table shows respective measurements of 20 workers along with hours of work per day and the area of the city the work took place. [You can use Excel-Data Analysis – Regression or http://vassarstats.net/multU.html] SBP Hrs/day Area 109.6 7 east 107.4 8 east 140.3 9 east 146.5 12 east 98.2 6 east 137.8 9 east 124.1 10 east 113.2 8 east 127.8 9 east 125.3 8 east 108.5 6 west 181.3 13 west 137.4 10 west 146.2 10 west 142.4 9 west 123.7 8 west 129.6 8 west 143.6 9 west 160.7 11 west 148.3 9 west a) What is the regression equation? b) Interpret the meaning of the slopes in this problem. d) At the 0.05 level of significance, determine whether each independent variable makes a contribution to the…
- which of the following regressions represents the strongest negative linear relationship between x and y? (Attached in picture provided)The data in Table 1 reports the aggregate consumption (Y, in billions) and disposable income (X, in billions) for the prosperous land of Kumandra. Draw a scatter diagram for the data and determine by inspection if there exists an approximate linear relationship between Y and X. Approximately draw a straight-line between the plotted values. Can we use this data for a linear regression model? Why?A materials engineer working for a furniture manufacturer wants to evaluate the rigidity of the particle board used by the manufacturer. The engineer collects stiffness data from pieces of particle board that have different densities at different temperatures. Determine the connection between the stiffness and the density of the wood. What does Pierson's r tell us? What is the regression between the stiffness and the density of the wood? Write the equation of the linear regression? density rigidity Temp 9.5 14.814 70.61056 8.4 17.502 73.34893 9.8 14.007 66.15377 11 19.443 70.05781 8.3 7.573 69.33919 9.9 14.191 69.12882 8.6 9.714 69.83351 6.4 8.076 64.36617 7 5.304 65.41039 8.2 10.728 67.76739 17.4 43.243 69.70053 15 25.319 66.93095 15.2 28.028 71.52362 16.4 41.792 66.60748 16.7 49.499 67.98685 15.4 25.312 64.29324 15 26.222 64.48343 14.5 22.148 71.3084 14.8 26.751 69.58755 13.6 18.036 71.13321 25.6 96.305 72.09707 24.4 72.594 67.32207…