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Q: Q4) Prove that dx 1+ 2 sinx || In √3 Χ tan tan x + 2 -√√3 +2 + √√3
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Q: Q4\ Find the average value of f(x,y) = (+√y) where 0 ≤ x ≤y and 0 ≤ y ≤ 4.
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- An engineer wants to determine how the weight of a gas powered car, x, affects gas mileage, y. The accompanying days represent the weights of various domestic cars and their miles per gallon in the city for the most recent model year. weight Miles per (pounds), x Gallon, y 3797 16 3897 16 2704 24 3608 20 3360 22 3040 22 3787 17 2618 24 3509 18 3798 16 3399 17 Find the least squares regression line treating weight as the explanatory variable and miles per gallon as the response variable. Find the least squares regression line treating weight as the explanatory variable and miles per gallon as the response variable. y hat = _____x + ______(Round the x…An insurance manager believes that the number of new policies written annually by his agents is related to the number of years of selling experience that these agents have. A random sample of 12 agents revealed the data in the table below: Number of years of experience Number of new policies written annually 2 17 5 22 7 34 6 37 12 50 9 41 5 13 20 48 13 39 4 20 10 35 20 63 2.1 determine the dependent and the independent variable 2.2 using appropriate computational formulae find the least-square regression line. 2.3 Interpret the y- intercepts of regression equation in question 2.2 above 2.4 Calculate the Pearson’s correlation coefficient for the above data 2.5 interpret the correlation coefficient calculate in question 2.4 above 2.6 Predict the number of policies written annually by an agent with 3 years of experience.Riboflavin (Vitamin B2) is determined in a cereal sample by measuring its fluorescence intensity(형광세기) in 5% acetic acid solution. A calibration curve was prepared by measuring the fluorescence intensities of a series of standards of increasing concentrations. The following data were obtained. Riboflavin (μg/mL) 0.000 0.100 0.200 0.400 0.800 Unknown sample Fluorescence intensity 0.0 5.8 12.2 22.3 43.3 15.4 (a) Use the method of least squares to obtain the best straight line through these five points (n=5). (b) Make a graph showing the experimental data and the calculated straight line. (c) An unknown sample gave an observed fluorescence intensity of 15.4. Calculate the concentration of Riboflavin (Vitamin B2) in the unknown sample (μg/mL). (d) Calculate the coefficient of determination (R2).
- Consider the table below which displays the price of a commodity for six consecutive years. Year Price (dollars) 1 250 2 255 3 253 4 255 5 259 6 261 Use the method of least squares to fit the model E(Yt) = β0+ β1t to the data. Write the prediction equation. Use the prediction equation to obtain forecasts of the prices in years 7 and 8. Find 95% prediction intervals for years 7 and 8.The population of Botswana (in millions) for the years 1970to 2020 is given in the table.Year 1970 1980 1990 2000 2010 2020Population, P 0.628 0.898 1.287 1.643 1.987 2.254(a) Make a scatter plot (population versus years) for the data. (b) Using the scatter plot determine the data trend and law of the curve ofbest fit for the data. (c) Use the least squares method find the curve of best fit for the data. (d) Hence estimate the population of Botswana in the year 2036Time to determine the temperature change along a wallcountermeasurements were taken. Using the least squares method,Describe the temperature change as a function of time with the data.t (min) 0 1 2 3 4 5 6T (o C) 20 23 33 34 56 79 98
- Consider the following model y = β0 + β1x + ∈, where y is the daily rate of return of a stock, and x is the daily rate of return of the stock market as a whole, measured by the daily rate of return of Standard & Poor's (S&P) 500 Composite Index. Using a random sample of n = 12 days from 2007, the least squares lines shown in the table below were obtained for four firms. The estimated standard error of 1 is shown to the right of each least squares prediction equation. Estimated Market Model & Estimated Std Error of β1 Company A y = .0010 + 1.40x, β1 = .03Company B y = .0005 - 1.21x, β1 = .06Company C y = .0010 + 1.62x 1.34, β1 = 1.34Company D y = .0013 + .76x .15, β1 = 0.15 Calculate the test statistic for determining whether the market model is useful for predicting daily rate of return of Company A's stock. a) 161.6b) 1.40 ± .067 c) 1.40d) 46.7A 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 following data pertain to the chlorine residual ina swimming pool at various times after it has been treatedwith chemicals:Number of Chlorine residualhours (parts per million)2 1.84 1.56 1.48 1.110 1.112 0.9 (a) Fit a least squares line from which we can predict thechlorine residual in terms of the number of hours sincethe pool has been treated with chemicals.(b) Use the equation of the least squares line to estimatethe chlorine residual in the pool five hours after it hasbeen treated with chemicals.
- In order to study the relationship between age and length of time that a smoker has been smoking, the following data were collected. x= age of a smoker y= years since he or she started smoking. x = y= 26 8 32 9 27 7 24 6 34 10 20 4 Compute the coorelation and find the least squares line.A tax collector wishes to see if the means of the values of the tax exempt properties are different for twolarge cities. The data are given in millions of dollars, use α = 0.05. Assume the populations are normallydistributed with unequal variances.City A 113 25 44 31 22 23 11 19 14 2City B 295 82 16 5 50 81 4 11 1) State the hypotheses. 2) Find the test statistic and Compute the critical value(s), then draw and label the curve. 3) Make the decision and Summarize the results.The following data show the number of hurricanes to directly strike a certain country each decade. A major hurricane is one with a strength rating of 3, 4 or 5. DecadeTotal Number of HurricanesNumber of Major Hurricanes1941 – 195021111951 – 19601881961 – 19701361971 – 19801241981 – 19901551991 – 20001452001 – 200493 Using only completed decades (1941 – 2000), calculate the least squares line for the number of major hurricanes expected based on the total number of hurricanes. (Round your answers to three decimal places.) ŷ = + x