Dynamic viscosity of water μ (10-³ N.) is related to temperature TCC) in the following manner: (let T = x; μ = y) T н O 5 1.787 1.519 10 1.307 20 30 40 1.002 0.7975 0.6529 a. Derive linear regression equation to fit a line to these data. Using the linear equation make prediction at T = 7.5°C b. Derive second order regression equation to fit a parabola to these data. Using the parabolic equation mak prediction at T = 7.5°C
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- XYZ Corporation Stock Prices The following table shows the average stock price, in dollars, of XYZ Corporation in the given month. Month Stock price January 2011 43.71 February 2011 44.22 March 2011 44.44 April 2011 45.17 May 2011 45.97 a. Find the equation of the regression line. Round the regression coefficients to three decimal places. b. Plot the data points and the regression line. c. Explain in practical terms the meaning of the slope of the regression line. d. Based on the trend of the regression line, what do you predict the stock price to be in January 2012? January 2013?Zipfs Law The following table shows U.S cities by rank in terms of population and population in thousands. City Rank r Population N New York 1 8491 Chicago 3 2722 Philadelphia 5 1560 Dallas 9 1280 Austin 11 913 San Francisco 13 852 Columbus 15 836 A rule known as Zipfs law tells us that it is reasonable to approximate these data with a power function. a Use power regression to express the population as a function of the rank. b Plot the data along with the power function from part a. c Phoenix is the sixth largest city in the United States. Use your answer from part a to estimate population of Phoenix. Round your answer in thousands to the nearest whole number. Note: The actual population is 1537 thousand.Let x be the size of a house (in square feet) and y be the amount of natural gas used (therms) during a specified period. Suppose that for a particular community, x and y are related according to the simple linear regression model with the following values. ? = slope of population regression line = 0.016 ? = y intercept of population regression line = −7 Question: Graph the population regression line by first finding the point on the line corresponding to x = 1,000 and then the point corresponding to x = 2,000, and drawing a line through these points.
- The estimated regression equation for a model involving two independent variables and 10 observations follows. y^=31.5111+0.5611x1+0.3254x2 a. Interpret b1b and b2 in this estimated regression equation (to 4 decimals ) b1____ b2____ b. Estimate y when x1=180 and x2=310 ( to 3 decimals)The measure of standard error can also be applied to the parameter estimates resulting from linear regressions. For example, consider the following linear regression equation that describes the relationship between education and wage: WAGEi=β0+β1EDUCi+εi where WAGEi is the hourly wage of person i (i.e., any specific person) and EDUCi is the number of years of education for that same person. The residual εi encompasses other factors that influence wage, and is assumed to be uncorrelated with education and have a mean of zero. Suppose that after collecting a cross-sectional data set, you run an OLS regression to obtain the following parameter estimates: WAGEi=−11.5+6.1 EDUCi If the standard error of the estimate of β1 is 1.32, then the true value of β1 lies between(4.78, 4.12, 3.46, 5.44) and (6.76, 7.42, 8.74) . As the number of observations in a data set grows, you would expect this range to (DECREASE , INCREASE) in size.A paddle wheel on a boat has a diameter of 5 meters and takes180 seconds to complete one revolution. As the wheel begins to turn, a barnacle attaches to the wheel at its lowest point, which is 0.5 meters below the surface of the water. a) Create a table of values that describes the height of the barnacle on the outer edge of the wheel during the first 12 minutes of the boat ride. b) Use your table of values to write a sinusoidal regression equation that models the height of the barnacle as a function of time. (Round to the nearest tenth). c) How does the radius of the paddle wheel relate to the parameters of your equation? Explain d) The barnacle falls off the wheel after 22.5 minutes. Use your regression equation to predict the height of the barnacle when it falls of the wheel, to the nearest tenth of a meter. e) Determine the total time within the first rotation that the barnacle is at least 2 meters above the surface of the water, rounded to the nearest tenth of a minute
- Life expectancy at birth is the estimated lifespan of a baby born in a particular year given the conditions of that time period. The regression line is y=0.205x-336, where x=birth year and y=US life male expectancy in years. The value of r2 is 0.981 a. use the regression line to estimate the US life expetancy of a male baby born in 1990, to the nearest tenth of a year. b. use the regression line to predict the US life expectancy of a male baby born in 2014, to the nearest tenth of a year. c. what is the slope regression line and what are the units of measurement?The least-squares regression equation is y=620.6x+16,624 where y is the median income and x is the percentage of 25 years and older with at least a bachelor's degree in the region. The scatter diagram indicates a linear relation between the two variables with a correlation coefficient of 0.7004. Interpret the slope.In regards to "Go to Stat > Regression > Regression > Fit a regression model." where is stat?
- Let X = height of the students in inches Let Y = Foot length of the students in centimeters Complete manual solutions for the SLRM coefficients, their interpretations and write down the best fitting linear regression equation. What is the predicted value of foot when height = 75?The estimate of b in the regression equation y=a+bx+error by the method of least square isThe least-squares regression equation is y=728.0x+14,705 where y is the median income and x is the percentage of 25 years and older with at least a bachelor's degree in the region. The scatter diagram indicates a linear relation between the two variables with a correlation coefficient of 0.8165. For every dollar increase in median income, the percent of adults having at least a bachelor's degree is ___%, on average. For a median income of $0, the percent of adults with a bachelor's degree is ____%.