The power (in microwatts) of a laser is measured as a function of current (in milliamps). Find the linear least-squares fit for thedata points.Current (milliamps)| 1.0 1.1 1.2 1.3 1.4 1.5Laser power (microwatts) 0.52 0.74 0.81 0.85 1.14 1.21Note that the coefficients of the linear first-square fit for f(x) = mx + b are determined by the following equations2x; + bn = y;mj3lj=lEx + b2x; =x;• yjmj=lj=lj=l(Use symbolic notation and fractions where needed. Give the coefficients to two decimal places.)f(x) =WI WI

Given: Data points, To find: Linear first-square fit f(x)=mx+b.

Answered: The power (in microwatts) of a laser is…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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The scatter plot below shows data for the average cost of a high-end computer (y, in dollars) in the year x years since 2000. The least squares regression line is given by yˆ=−1677+314x. A coordinate plane has a horizontal x-axis labeled Year from 4 to 12 in increments of 2 and a vertical y-axis labeled Cost in dollars from 0 to 2000 in increments of 500. The following points are plotted: left-parenthesis 6 comma 250 right-parenthesis, left-parenthesis 7 comma 550 right-parenthesis, left-parenthesis 9 comma 1000 right-parenthesis, left-parenthesis 10 comma 1300 right-parenthesis, and left-parenthesis 11 comma 2000 right-parenthesis. A line rises from left to right, passing through left-parenthesis 7 comma 550 right-parenthesis and left-parenthesis 10 comma 1500 right-parenthesis. All coordinate are approximate. Interpret the slope of the least squares regression line. Select the correct answer below: On average, the average cost of a high-end computer is…
An aerabk exercise instructor remembars the data givan in the follawing table, which shows the recommanded maximum exercise haart rates for individuals of the given ages. (A graphing calculator is recommended.) Age (x years) 20 40 60 Maximum heart rate 172 155 138 (y bente per minute) (a) Find the lincar corelation coefficient for the deta. (Rcund your answer to two decimal places.) (b) What is the signiticance of the value found in part (a)? O The slope of the regression is about half of what the expected value is. O The graph of the regression points passes through nene of the data points. * The graph of the regression points passes through all three data peints. O One of the data points is the y-intercept. O The linear correlation cooficient should always be positive. (c) Find the equetion of the leest-squeres regression line. (Round your answers to two decimal pleces.) (d) Use the equation of the least-squares line from part (c] te predict the maximum cxercise heart rate fer a…
study investigated how the content of vitamin A in carrots is affected by the time being cooked. In this example: X represents the amount of time, in minutes, that the carrot slices were cooked Y represents the content of vitamin A (in milligrams) in the carrot slices The least-squares regression equation for this relationship is: Y = 22.4 – 0.65X Using the regression equation, predict the vitamin A content (in milligrams) for a carrot slice that was cooked for 15 minutes. Provide your answer as a numeric value rounded to two decimal places.
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The number of banks in a country has been dropping steadily since 1984, and the trend in recent years has been roughly linear. The annual data for the years 1999 through 2008 can be summarized as follows, where x represents the years since 1990 and y the number of banks, in thousands. n=10 Ex-235 ²-5605 Ey-77.564 Ey²=603.80424 Exy-1810.155 a. Find an equation for the least squares line. b. Use your result from part a to predict the number of banks in the year 2020. c. If this trend continues linearly, in what year will the number of banks drop below 6200? d. Find and interpret the correlation coefficient.
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