A chemical company wishing to study the effect of extraction time on theefficiency of an extraction operation, obtained the data shown in the followingtable.Extraction time( minutes ) x2745 4119353919491531Extractionefficiency (1%)y57648046627252775768Fit a straight line to the given data by the method of least squares and use itsto predict the extraction efficiency one can expect when the extraction timeis 35 minutes.

Answered: Image /qna-images/answer/636e46b7-3dce-4d21-b853-77e7a4efe4c9.jpg

Answered: Fit a straight line to the given data…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.3: Lines

Problem 76E

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If your graphing calculator is capable of computing a least-squares sinusoidal regression model, use it to find a second model for the data. Graph this new equation along with your first model. How do they compare?
Ordinary least squares method was used to fit a regression model to predict income (in thousands of dollars) from the following predictors: X1 = education X2 = gender (where male = 0 and female = 1) X3 = interaction between education and gender %3D The model produced the following coefficients: B, = -11.52, B, = 2.99, ß, = 1.01, ßz = -0.94. On average, how much income do men and women get if they have 20 years of education? Key A Men: $48.28 thousand; Women: $30.49 thousand B Men: $48.28 thousand; Women: $28.08 thousand C Men: $59.80 thousand; Women: $41.00 thousand D Men: $59.80 thousand; Women: $20.20 thousand
Interpret the least squares regression line of this data set. Meteorologists in a seaside town wanted to understand how their annual rainfall is affected by the temperature of coastal waters. For the past few years, they monitored the average temperature of coastal waters (in Celsius), x, as well as the annual rainfall (in millimetres), y. Rainfall statistics • The mean of the x-values is 11.503. • The mean of the y-values is 366.637. • The sample standard deviation of the x-values is 4.900. • The sample standard deviation of the y-values is 44.387. • The correlation coefficient of the data set is 0.896. The correct least squares regression line for the data set is: y = 8.116x + 273.273 Use it to complete the following sentence: The least squares regression line predicts an additional annual rainfall if the average temperature of coastal waters increases by one degree millimetres of Celsius.
A regression line was calculated to relate the length (cm) of newborn boys to their weight in kg. The least squares regression line is weight = -5.94 + 0.1875 length. Explain in words what this model means (slop and intercept) The new- born boy was 48 cm long, what is the predicted weight of this boy? It is known that the boy is weighed 3 kg. what was his residual? What does that say about him?
Use the least squares regression line of this data set to predict a value. Meteorologists in a seaside town wanted to understand how their annual rainfall is affected by the temperature of coastal waters. For the past few years, they monitored the average temperature of coastal waters (in Celsius), x, as well as the annual rainfall (in millimetres), y. Rainfall statistics • The mean of the x-values is 11.503. • The mean of the y-values is 366.637. • The sample standard deviation of the x-values is 4.900. • The sample standard deviation of the y-values is 44.387. • The correlation coefficient of the data set is 0.896. The least squares regression line of this data set is: y = 8.116x + 273.273 How much rainfall does this line predict in a year if the average temperature of coastal waters is 15 degrees Celsius? Round your answer to the nearest integer. millimetres
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.
I ONLY NEED PART C,D, and E answered please thanks A regression was run to determine if there is a relationship between the happiness index (y) and life expectancy in years of a given country (x).The results of the regression were: ˆyy^=a+bxa=-1.102b=0.074 (a) Write the equation of the Least Squares Regression line of the formˆyy^= + x(b) Which is a possible value for the correlation coefficient, rr? -0.858 -1.07 1.07 0.858 (c) If a country increases its life expectancy, the happiness index will decrease increase (d) If the life expectancy is increased by 2.5 years in a certain country, how much will the happiness index change? Round to two decimal places._____(e) Use the regression line to predict the happiness index of a country with a life expectancy of 63 years. Round to two decimal places._______Use the space below to type your answer AND/OR to upload a picture of your work for all the questions in this problem.
A random sample of 65 high school seniors was selected from all high school seniors at a certain high school. The following scatterplot shows the height, in centimeters (cm), and the foot length, in cm, for each high school senior from the sample. The least-squares regression line is shown. The computer output from the least-squares regression analysis is also shown. Term Coef(SE) CoefT-ValueP-Value Constant 105.086.0017.510.000 Foot length 2.5990.23810.920.000 S=5.90181R–sq=65.42% (a) Calculate and interpret the residual for the high school senior with a foot length of 20cm and a height of 160cm. BoldItalicUnderlineSuperscriptSubscriptUndoRedoΩBullet listNumbered listImage (12 image limit) Edit imageView imageDelete image Question 2 (b) The standard deviation of the residuals is s=5.9. Interpret the value in context. BoldItalicUnderlineSuperscriptSubscriptUndoRedoΩBullet listNumbered listImage (12 image limit) Edit imageView imageDelete…
The output table below represents the results of the estimation of household expenditures (Y) and income (X) in thousand dollars. Considering the results, answer the following questions. Dependent Variable: Y Method: Least Squares Date: 01/07/16 Time: 11:22 Sample: 2000 2015 Included observations: 16 Variable Coefficient Std. Error t-Statistic Prob. C -0.241942 2.452237 -0.098662 0.9228 X 0.363176 0.013890 26.14674 0.0000 R-squared 0.979933 Mean dependent var 55.43750 Adjusted R-squared 0.978499 S.D. dependent var 33.17221 S.E. of regression 4.864079 Akaike info criterion 6.118100 Sum squared resid 331.2297 Schwarz criterion 6.214674 Log likelihood -46.94480 Hannan-Quinn criter. 6.123046 F-statistic 683.6522 Durbin-Watson stat 0.632113…
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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Fit a straight line to the given data by the method of least squares and use its to predict the extraction efficiency one can expect when the extraction time is 35 minutes.