The following are the annual profits in thousands in a certain business: Year 2001 2002 2003 2004 2005 2006 2007 Profit (thousands) 75 65 80 85 95 60 72 By the method of least squares, fit a straight line using that estimate profit for 2011.
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- The following are the scores that 12 students obtainedon the midterm and final examinations in a course instatistics:Midterm examination Final examinationx y71 8349 6280 7673 7793 8985 7458 4882 7864 7632 5187 7380 89 (a) Find the equation of the least squares line that willenable us to predict a student’s final examination score inthis course on the basis of his or her score on the midtermexamination.(b) Predict the final examination score of a student whoreceived an 84 on the midterm examination.When a least squares line is fit to the 12 observations in the labor cost data, we obtain SSE =656, 214.3589. Calculate s2 and s (isnt n-k-1)?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.
- 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 isPercentages of public school students in fourth and eighth grades who were above the proficiency level were given for 8 western states 4th Grade Proficiency 8th Grade Proficiency Arizona 15 21 California 11 18 Hawaii 16 16 Montana 22 37 New Mexico 13 13 Oregon 21 32 Utah 23 26 Wyoming 19 25 Construct a scatterplot and comment on any interesting characteristics Find the least squares equation. If Nevada had a 4th grade proficiency of 14%, what would you expect the 8th grade proficiency to be?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.
- The following table is an abbreviated life expectancy table for males. current age, x 0 20 40 60 80 life expectancy, y 76.6 years 78.9 years 80.5 years 81.7 years 82.7 years a. Find the straight line that provides the best least-squares fit for these data.A regression analysis between sales (in $1000) and advertising (in $100) resulted in the following least squares line: ŷ = 75 + 6x. This implies that if advertising is $800, then the predicted amount of sales (in dollars) is Select one: a. $12,300 b. $123,000 c. $4,875 d. $4,875,000The following data show the amount spent on office-building construction (in thousands) for a particular county during a 6-month period. Office Construction Month Apr May Jun Jul Aug Sep Amount (in thousands) $15 $25 $42 $51 $60 $74 Copy Data Find the least‑squares regression line for the data. (Let x=1 correspond to January, x=2 to February, etc.) Round the coefficients to three decimal places. Estimate the amount spent on construction in October. Express your answer in thousands of dollars and round to three decimal places.
- An agricultural scientist planted alfalfa on several plots of land, identical except for the soil pH. Following are the dry matter yields (in pounds per acre) for each plot. pH 4.6 4.8 5.2 5.4 5.6 5.8 6 Yield 1056 1833 1629 1852 1783 2647 2181 Compute the least-squares line for predicting yield from pH. Round the answers to two decimal places. y = + xThe following data show the amount spent on office-building construction (in thousands) for a particular county during a 66-month period. Office Construction Month Apr May Jun Jul Aug Sep Amount (in thousands) $14 $26 $40 $46 $60 $69 Find the least‑squares regression line for the data. (Let x=1x=1 correspond to January, x=2x=2 to February, etc.) Round the coefficients to three decimal places. Estimate the amount spent on construction in October. Express your answer in thousands of dollars and round to three decimal places.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)