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- In a study of copper bars, the relationship between shear stress in ksi (x) and shear strain in % (y) was summarized by the least-squares line y = −20.00 + 2.56x. There were a total of n = 18 observations, and the coefficient of determination was r 2 = 0.9111. If the total sum of squares was ∑ni=1(yi−y⎯⎯)2∑i=1n(yi−y¯)2 = 234.19, compute the estimated error variance s2. Round the answer to three decimal places.Compute the sum-of-squares error (SSE) by hand for the given set of data and linear model. (4, 4), (7, 7), (9, 10); y = x − 1Find the curve of best-fit y = axb to the following data by using the method of least square.
- Suppose a least-squares regression line is given by y=4.302x−3.293. What is the mean value of the response variable if x=20? μy20=_______? (Round to one decimal place as needed.)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.In the manufacture of synthetic fiber, the fiber is often “set” by subjecting it to high temperatures. The object is to improve the shrinkage properties of the fiber. In a test of 23 yarn specimens, the relationship between temperature in °C (x) and shrinkage in % (y) was summarized by the least-squares line y = −12.789 + 0.133x. The total sum of square was ∑ni=1(yi−y⎯⎯)2∑i=1n(yi−y¯)2 = 57.313, and the estimated error variance was s2 = 0.0670. Compute the coefficient of determination r 2. Round the answer to three decimal places.
- Each of the following pairs represents the number of licensed drivers (X) and the number of cars (Y) for seven houses in my neighborhood: Drivers X Cars Y 5 4 5 3 2 2 2 2 3 2 1 1 2 2 Construct a scatterplot to verify a lack of pronounced curvilinearity. Determine the least squares equation for these data. (Remember, you will first have to calculate r, SSy, and SSx) Determine the standard error of estimate, sy|x, given that n = 7. Predict the number of cars for each of two new families with two and five drivers.Suppose Wesley is a marine biologist who is interested in the relationship between the age and the size of male Dungeness crabs. Wesley collects data on 1,000 crabs and uses the data to develop the following least-squares regression line where ? is the age of the crab in months and ?̂ is the predicted value of ?, the size of the male crab in cm. ?̂=8.2052+0.5693? What is the value of ?̂ when a male crab is 21.7865 months old? Provide your answer with precision to two decimal placeThe data regarding the production of wheat in tons (X) and the price of the kilo of flour in Ghana cedis (Y) Takoradi some years ago were: a. Fit the regression line for the day using the method of least squares
- The position of a particle x(t) on an axis has been monitored. The results are shown in the following table. t x(t)0 41 114 129 12 By the least squares method, fit the data to a quadratic model: Report x(10)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 ? (in cubic feet) to heat the home and outside temperature ? (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 ? from ? and found it to be ?̂ =85+16?. By looking at the equation of the least‑squares regression line, you can see that the correlation between amount of gas used and degree‑days isSuppose 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.)