solve all part and show all the work paper solution only 8. A study looks to model the effects of temperature on the snowman population in Ottawa,Ontario. The following table lists the average monthly temperature and the estimatedsnowman population in the Ottawa area for November through March.MonthTemperature (°C)Snowmen (hundreds)Nov-23.2DecJanFeb-10-14-1312.4 16.2 14.8Mar-76.4a.) Using the method of Least Squares, find the linear equation, describing the numberof snowmen as a function of temperature, that best fits the given data.b.) Based on your linear model, at what temperature would you expect there to be nosnowmen?

Given data: Month Nov Dec Jan Feb Mar Temperature °C -2 -10 -14 -13 -7 Snowmen (hundreds) 3.2…

Answered: 8. A study looks to model the effects…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.3: Least Squares Approximation

Problem 31EQ

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The accompanying data resulted from an experiment in which weld diameter x and shear strength y (in pounds) were determined for five different spot welds on steel. A scatterplot shows a pronounced linear pattern. The least-squares line is = -964.98 + 8.60x. Because 1 lb = 0.4536 kg, strength observations can be re-expressed in kilograms through multiplication by this conversion factor: new y = 0.4536(old y). What is the equation of the least-squares line when y is expressed in kilograms? (Give the answer to two decimal places.) = x 202.9 212.9 222.9 232.9 242.8 y 814.5 786.1 961.2 1118.8 1077.0
A lab received a new instrument to measure pH. To compare the new instrument to the old lab instrument, 11 samples were measured with both pieces of equipment. Using the data (below), find the least squares equation (x = "pH old" and Y = "pH new") and then predict the value on the new instrument if the old instrument gave a pH of 6.30. Enter your answer using 3 significant digits. pH Old pH New 6.35 6.16 6.01 5.95 6.15 6.05 6 6.01 6.11 6.06 5.93 5.83 5.84 5.81 5.63 5.71 5.63 5.74 6.11 6.1 6.07 6.01
The following gives the number of accidents that occurred on Florida State Highway 101 during the last 4 months: Month Jan Feb Mar Apr Number of Accidents 25 45 70 95 Using the least-squares regression method, the trend equation for forecasting is (round your responses to two decimal places): y = 0 + 23.5 x Using least-squares regression, the forecast for the number of accidents that will occur in the month of May = accidents (enter your response as a whole number).
Find the equation of the least-squares line for the stride length and speed of camels given in the table below. Use the equation of the least-squares line from to predict the average speed (in meters per second) of a camel with a stride length of 3.7 meters. Round your results to the nearest tenth of a meter per second.
Fit a straight line trend by the method of least squares for the following consumer price index numbers of the industrial workers. Year 2010 2011 2012 2013 2014 Index number 166 177 198 221 225
7) An accountant wishes to predict direct labor cost (y) on the basis of the batch size (x) of a product produced in a job shop. Using data for 12 production runs, the least squares line has an intercept of 18.488 and a slope of 10.146. Please interpret the meanings of the intercept and the slope in this context. Do you think that the interpretation of the intercept does make practical sense?
Assume that the table below displays the number of freight tonnes carried (in millions) in Australia between 1990 and 2015.Year199019952000200520102015Number of freight tonnes (millions)6684104126160186a) Draw a scatter diagram of the data.b) Find the least squares regression line of number of freight tonnes (in millions) carried on a year. (Note: Use only the last two digits of the year).c) Draw the line in (b) on the scatter diagram in (a). Comment on whether you feel the line is a good fit of the data.d) Use the line in (b) to predict the number of freight tonnes that might be carried in Australia in both 2020 and 2025.e) Do you think your predictions in (d) will be relatively accurate? Why or why not?
B- Find the least squares line approximating the data in the following table: 7 9 10 12 4 y 2.5 ----
An engineer is testing a new car model to determine how its fuel efficiency, measured in L/(100 km), is related to its speed, which is measured in km/hour. The engineer calculates the average speed for 30 trials. The average speed is an example of a (statistic or parameter) The engineer would like to find the least squares regression line predicting fuel used (y) from speed (x) for the 30 cars he observed. He collected the data below. Speed 62 65 80 82 85 87 90 96 98 100 Fuel 12 13 14 13 14 14 15 15 16 15 Speed 100 102 104 107 112 114 114 117 121 122 Fuel 16 17 16 17 18 17 18 17 18 19 Speed 124 127 127 130 132 137 138 142 144 150 Fuel 18 19 20 19 21 23 22 23 24 26 The regression line equation is Round each number to four decimal places.
What is the least-squares line approximation to a set of datapoints? How is the line determined?
In a study of 2005 model cars, a researcher computed the least squares regression line of miles per gallon (mpg) on weight (in pounds). They obtained the following equation for this line: mpg = 34.576 - 0.007weight Based on the least-squares line, we would predict a 2005 model car with weight equal to 3,000 pounds would have a mpg of Fill in the blank with: ##.###
Suppose the manager of a gas station monitors how many bags of ice he sells daily along with recording the highest temperature each day during the summer. The data are plotted with temperature, in degrees Fahrenheit (F), as the explanatory variable and the number of ice bags sold that day as the response variable. The least squares regression (LSR) line for the data is Bags = -151.05 +2.65Temp. On one of the observed days, the temperature was 82 °F and 68 bags of ice were sold. Determine the number of bags of ice predicted to be sold by the LSR line, Bags, when the temperature is (82\ \text (°F. J\\) Enter your answer as a whole number, rounding if necessary. Bags = 1.11 residual Incorrect Using the predicted value you just found, compute the residual at this temperature. 1.11 Incorrect ice bags ice bags

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