For the following data. X 1.7 3.24 4.8 6.93 y 1.11 1.39 2.73 3.13 a. Find the newton interpolating polynomial (in general form) using a divided difference table. b. Find the least squares line and the corresponding r2 value. c. Find the least squares parabola and the corresponding r value. d. Using the equations of b and c , estimate the value of y for: i. x = 4.00, provide a brief discussion. ii. x = 7.00, provide a brief discussion.
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- bThe average rate of change of the linear function f(x)=3x+5 between any two points is ________.The regression line for a data set showing the monthly utility bill U in a certain city versus the square footage F of the residence is given by U = 0.2F − 100 dollars. What monthly utility bill would be expected for a 2500 square foot home in this city? $The following data shows the atmospheric pollutants yi(relative to an EPA standard) at half hour interval xi. Find the equation y=a+bx of the least square line that best fits the data points given by 2,1, 5,2, 7,3, 8,3. Hence predict the atmospheric pollutant at x=6 half hour.
- Suppose you are given the following (x, y) data pairs.x 1 2 5y 4 3 8 a) Find the least-squares equation for these data (rounded to four digits after the decimal). y = _____ + _____Suppose you are given the following (x,y) data pairs. X 1 3 4 Y 4 3 7 find the least squares equation for these data(rounded to four digits after the decimal) y=___+____xsuppose you are given these (x, y) data pairs.x 4 3 8y 1 2 5 a)Find the least-squares equation for these data (rounded to four digits after the decimal). ŷ = ______+ _____x
- The ages, t years of 7 hospital patients and their blood pressure, p mmHg are shown in Table 3.Table 3 a b c d e f g t 42 74 48 35 56 26 60 p 98 130 120 88 182 80 135 c) Determine the intercept of the regression line correct to 3 decimal points.(d) Find the equation of the least square regression of p on t.(e) Estimate the blood pressure of a 40-year old patient.Use the given data to find a regression line that best fits the total annual cost data for cost C in dollars as a function of the production level x widgets. Here, cost is the dependent variable, and production level is the independent variable. Find the regression function for cost, and write it as C ( x ) = m x + b, where m is rounded to the nearest tenth, and b is rounded to the nearest tenth. Enter the value for m, rounded to the nearest tenth. Enter the value for b, rounded to the nearest tenth. Use the regression function C ( x ) = m x + b with m rounded to the nearest tenth and b rounded to the nearest tenth. Compute C ( 45 ), rounded to the nearest tenth. Use the regression function C ( x ) = m x + b with m rounded to the nearest tenth and b rounded to the nearest tenth. Compute C ( 0 ), rounded to the nearest tenth.The following table shows the rate R of vehicular involvement in traffic accidents (per 100,000,000 vehicle-miles) as a function of vehicular speed s, in miles per hour, for commercial vehicles driving at night on urban streets. Speed s Accident rate R 20 1500 25 700 30 250 35 300 40 750 45 1400 (a) Use regression to find a quadratic model for the data. (Round the regression parameters to two decimal places.) R = 7.79s2−514.36s+8733.57 (b) Calculate R(70). (Round your answer to two decimal places.) R(70) = Explain what your answer means in practical terms. Commercial vehicles driving at night on urban streets at miles per hour have traffic accidents at a rate of per 100,000,000 vehicle miles.
- Assume that it costs that same company approximately C ( x ) =62,229+5,573x +0.033x 2 dollars to manufacture x of their new and imporved deluxe game play stations in an hour. Find and use the average cost function, C ¯ ( x ), to find the average cost to produce the first 4,454 deluxe stations rounded to the nearest cent (that is two decimal places).The following regression model describes the relation between the number of days of experience in a job involving the wiring of electronic components and the number of components which were rejected stack N u m b e r space o f space r e j e c t s with hat on top equals 249 minus 1.4 space D a y s space o f space e x p e r i e n c e Based on this model, estimate the number of components rejected for an employee with 97 days of experience in the job. Round your answer to one decimal place.The following table shows the rate R of vehicular involvement in traffic accidents (per 100,000,000 vehicle-miles) as a function of vehicular speed s, in miles per hour, for commercial vehicles driving at night on urban streets. Speed s Accident rate R 20 1600 25 600 30 200 35 300 40 800 45 1250 (A) Use regression to find a quadratic model for the data. (Round the regression parameters to two decimal places.) R =