For the data set below (a) Determine the least-squares regression line (b) Graph the least-squares regression line on the scatter diagram 3 4 6 8 4 6 11 16 (a) Determine the least-squares regression line ) (Round to four decimal places as needed) y =x Enter your answer in the ed it fields and then click Check Answer part 1 remaining e Type here to search X
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- The number of inches that a recently built structure sits on the ground is given by (image) where x is its age in months. a) Create a scatter plot to verify that it is reasonable to assume that the regression of Y on x is linear.b) Fit a straight line using the method of least squares. c) Use the least squares method to estimate alpha.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?Table gives life expectancies for people born in the United States in the given years. (a) Determine the least squares approximating line for these data and use it to predict the life expectancy of someone born in 2000. (b) How good is this model? Explain.
- An owner of a home in the Midwest installed solar panels to reduce heating costs. After installing the solar panels, he measured the amount of natural gas used y (in cubic feet) to heat the home and outside temperature x (in degree-days, where a day's degree-days are the number of degrees its average temperature falls below 65° F) over a 23-month period. He then computed the least-squares regression line for predicting y from x and found it to be ŷ = 85 + 16x. The software used to compute the least-squares regression line for the equation above says that r2 = 0.98. This suggests which of the following? 1. Gas used increases by square root of 0.98 = 0.99 cubic feet for each additional degree-day? 2. Although degree-days and gas used are correlated, degree-days do not predict gas used very accurately. 3. Prediction of gas used from degree-days will be quite accurate.Fit a curve of the form g(x) = A10Bx to the dataset using the Least Squares Method. Calculate the corrected values and the total squared error.(a) sketch the line that appears to be the best fit for the given points, (b) find the least squares regression line, and (c) determine the sum of squared error.
- A manager at the Camden Walmart is interested in learning more about the relationship between the number of customers in a checkout line and the total time it takes to check out. She selects a random sample of 11 customers and measured the number of customers who were in front of the selected customer in line and the time until that customer had finished checking out. An analysis of the data is provided below. Identify and interpret the y-intercept of the least squares regression line in context. Identify the coefficient of determination, r2. Interpret it in context. One of the data points appears to be an outlier. Describe this point and explain why it is considered an outlier.An engineer wants to determine how the weight of a gas-powered car, x, affects gas mileage, y. The accompanying data represent the weights of various domestic cars and their miles per gallon in the city for the most recent model year. Complete parts (a) Find the least-squares regression line treating weight as the explanatory variable and miles per gallon as the response variable.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…
- A magazine publishes restaurant ratings for various locations around the world. The magazine rates the restaurants for food, decor, service, and the cost per person. Develop a regression model to predict the cost per person, based on a variable that represents the sum of the three ratings. The magazine has compiled the accompanying table of this summated ratings variable and the cost per person for 25 restaurants in a major city. Assuming a linear relationship, use the least-squares method to compute the regression coefficients b0 and b1.A researcher at a large company has collected data on the beginning salary and current salary of 50 randomly selected employees. The correlation between the data sets is r = 0.912. The summary statistics from the data collected are shown bellow: Beginning Salary Ending Salary Mean x¯=56,340 y¯=82,070 Standard deviation Sx = 5,470 Sy = 7,800 Use a complete sentence to describe the strength and direction of the linear relationship between beginning salary and current salary. Find the equation of the least-squares regression line. (Round to two decimal places)A study of IT companies has found the following data on the age of each company and its annual volume of sales: Age (years) Sales (000) 2 22 2.5 34 3 33 4 37 4.5 40 4.5 45 5 49 3 30 6 58 6.5 58 (a) Determine the least squares regression that relates the age of company variable to the sales variable in the form y = a + bx. (b) Provide a practical interpretation of the coefficients a and b. (c) Determine the ‘goodness of fit’ (R2) of the estimated regression line. d) Using the estimated regression line determined in (a), calculate what volume of sales would be predicted for a company that is 3.5 years of age. (e) If it was found that…
