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- 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.Given are five observations for two variables, x and y. xi 3 8 12 18 20 yi 54 57 50 24 11 -select your answer choices- b. The least squares line provided an (good, bad) fit; __ % of the variability in y has been explained by the estimated regression equation (to 1 decimal)Compute the sum-of-squares error (SSE) by hand for the given set of data and linear model. (6, 6), (7, 7), (9, 10); y = x − 1
- The following data represent a company’s yearly sales volume and its advertising expenditure over a period of 5 years. (Y) (X) Sales in Millions Advertising Of Dollars in ($10,000) 15 32 16 33 18 35 17 34 16 36 Develop a scatter diagram of sales versus advertising and explain what it shows regarding the relationship between sales and advertising. Use the method of least squares to compute an estimated regression line between sales and advertising by computing b0 and b1The following data represent the number of flash drives sold per day at a local computer shop andtheir prices.Price (x) Units Sold (y)$34 336 432 635 530 938 240 1 a. Develop a least squares regression line and explain what the slope of the line indicates.b. Compute the coefficient of determination and comment on the strength of relationship betweenx and y.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.
- ou are given the following information about x and y. X Independent Variable Y Dependent Variable 15 5 12 7 10 9 7 11 The least squares estimate of b1 equals [3 decimals] ___________ The least squares estimate of b0equals _______________ The sample correlation coefficient equals _________A regression analysis between sales (y in $1000) and advertising (x in $100) resulted in the following least-squares line: yˆ ? 85 ? 7x. Given this information, if advertising costs were $600, what could we reasonably expect the amount of sales (in dollars) to be?The maximum discount value of the Entertainment® card for the “Fine Dining”section, Edition 10, for various pages is given below. Page number Maximum value ($)4 1614 1925 1532 1743 1957 1572 1685 1590 17What is the slope of the least squares (best-fit) line? Interpret the slope. What is the intercept of the least squares (best-fit) line? Interpret theintercept.
- The following table gives retail values of a 2017 Corvette for various odometer readings. Odometer Reading Retail Value ($) 13,000 52,525 18,000 51,675 20,000 51,400 25,000 50,475 29,000 49,825 32,000 49,275 (a) Find the equation of the least-squares line for the data. (Where odometer reading is the independent variable, x, and retail value is the dependent variable. Round your numerical values to two decimal places.) ŷ = (b) Use the equation from part (a) to predict the retail price of a 2017 Corvette with an odometer reading of 30,000. Round to the nearest $100. $ (c) Find the linear correlation coefficient for these data. (Round your answer to four decimal places.) r =The following table shows how many weeks a sample of 6 persons have worked at an automobile inspection station and on any given day: a) Find the least squares estimators and the values for a and b ??? = ___________ ? = ___________ ??? = ___________ ? = ___________ ??? = ___________ b) Determine AND WRITE the equation for the best fit line. c) Find the correlation coefficient, r, and describe the relationship between weeks in the program and time improvement.A study was conducted to detemine whether a the final grade of a student in an introductory psychology course is linearly related to his or her performance on the verbal ability test administered before college entrance. The verbal scores and final grades for 10 students are shown in the table below. Student Verbal Score x Final Grade y 1 30 39 2 58 69 3 57 70 4 35 42 5 69 83 6 75 93 7 51 62 8 56 63 9 25 27 10 50 63 Find the least squares line. y^= + x Should the regression be used to predict the final grade of a student with a verbal score of 100? answer: