7. Determine the equation, which will represent the best line for the following set of data and plot the graph of the equation in an MS Excel worksheet. Method of Least Squares Y XX ху 1 4.6 2 1 7.1 1 7.1 2 9.5 4 19.0 4 3 11.5 9 34.5 5 4 13.7 16 54.8 6 5 15.9 25 79.5 7 18.6 36 111.6 8 7 20.9 49 146.3 8 23.5 64 188.0 10 25.4 81 228.6
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- Suppose 5 out of 25 data points in a weighted least-squares problem have a y-measurement that is less reliable than the others, and they are to be weighted half as much as the other 20 points. One method is to weight the 20 points by a factor of 1 and the other 5 by a factor of 1/2. A second method is to weight the 20 points by a factor of 2 and the other 5 by a factor of 1. Do the two methods produce different results? Explain.The regional transit authority for a major metropolitan area wants to determine whetherthere is any relationship between the age of a bus and the annual maintenance cost. Asample of 10 buses resulted in the following data. Age of Bus (year) Maintenance Cost ($) 1 350 2 370 2 480 2 520 2 590 3 550 4 750 4 800 5 790 5 950 a. Develop the least squares estimated regression equation.b. Test to see whether the two variables are significantly related with α = .5.c. Did the least squares line provide a good fit to the observed data? Explain.d. Develop a 95% prediction interval for the maintenance cost for a specific bus thatis 4 years old.Select the equation of the least squares line for the data: (51.00, 1.0), (48.75, 2.5), (52.50, .5), (46.50, 5.0), (45.00, 4.5), (41.25, 6.5), (43.50, 5.0). a) ŷ = -28.956 − 0.54067x b) ŷ = 28.956 − 0.59474x c) ŷ = 0.54067x − 28.956 d) ŷ = 31.852 − 0.59474x e) ŷ = 28.956 − 0.54067x f) None of the above
- The following table shows the percent of water and the number of calories in various canned soups to which 100 g of water are added. (show all the necessary solution) Percent Water in Soups % Water Calories 83.3 28 92.3 26 91.9 39 89.4 57 89.5 57 90.5 36 91.9 32 91.7 32 a. Find the equation of the least squares line for the data. b. Use the equation in part a to find the expected number of calories in a soup that is 87% water. c. Determine the correlation coefficient of the data.Determine the best (according to sum-of-squares-measure) curve y = Aebx, through the dataabove.Transformed equationln(y) = ln(A) + bxorY = a + bx.A pediatrician wants to determine the relationship that exists between achild’s height, x, and head circumference, y. She randomly selects 11 children from her practice, measures their heights and head circumferences, and conducts the least-squares regression analysis with the simple linear model using StatCrunch. The output is given below: (a) Write down the equation of the least-squares regression line treating height as the explanatory variable and head circumference as the response variable. (b) Interpret the slope and y-intercept, if appropriate. (c) Use the regression equation to predict the head circumference of a child who is 25 inches tall. Assume that the regression model is applicable.(d) It is observed that one child who is 25 inches tall has a head circumference of 17.5 inches. Is the observed value above or below average among all children with heights of 25 inches?
- What is the least-squares line approximation to a set of datapoints? How is the line determined?Suppose a doctor measures the height, x, and head circumference, y, of 8 children and obtains the data below. Thecorrelation coefficient is 0.944 and the least squares regression line is y = 0.199x + 11.982. Complete parts (a) and (b)below.Height, x27.5 25.5 26.25 25.25 27.5 26.25 26 27.25 27.25 27 27.25 ФHead Circumference, # 17.5 17.0 17.2 17.0 17.5 17.3 17.2 17.4 17.3 17.3 17.4(a) Compute the coefficient of determination, R?R?.% (Round to one decimal place as needed.)(b) Interpret the coefficient of determination and comment on the adequacy of the linear model.Approximately % of the variation inis explained by the least-squares regression model.According to the residual plot, the linear model appears to be (Round to one decimal place as needed.)After deciding on the appropriateness of a linear model relating coffee sales and maximum temperature, the managers calculate the equation of the least-squares regression line to be =y−2553.5211.33x . This is the line shown in the scatter plot above.Based on the sample data and the regression line, complete the following. (a)For these data, temperature values that are less than the mean of the temperature values tend to be paired with coffee sales values that are ▼(Choose one) the mean of the coffee sales values. (b)According to the regression equation, for an increase of one degree in temperature, there is a corresponding ▼(Choose one) of 11.33 dollars in coffee sales. (c)What was the observed coffee sales value (in dollars) when the temperature was 39.6 degrees Fahrenheit? (d)From the regression equation, what is the predicted coffee sales value (in dollars) when the temperature is 39.6 degrees Fahrenheit? (Round your answer to at least…
- The following data is about the number of turns required to break a certain type of forged alloy bar, as well as the percentages of two alloying elements present in the metal. A) Fit a least squares regression plane and use its equation to estimate the number of turns required to break one of the bars, when x1 = 2.5 and x2 = 12 In the tabley = number of turnsx1 =% of element Ax2 =% of element B1) -Describe the association between College Tuition and Median Student Loan Debt for Graduates based on the scatter plot.-Identify and interpret the y-intercept and slope of your least squares regression line -Identify and interpret your coefficient of determination1. Prior to being hired, the ve salespersons for a computer store were given a standard sales aptitude test. For each individual, the score achieved on the aptitude test and the number of computer systems sold during the first 3 months of their employment are shown in the attached image. (a) Determine the least-squares regression line and interpret its slope. (b) Estimate, for a new employee who scores 60 on the sales aptitude test, the number of units the new employee will sell in her first 3 months with the company. (c) Find the standard error of estimate. (d) Find the r-square of the model.
