Question

It is thought that prehistoric Indians did not take their best tools, pottery, and household items when they visited higher elevations for their summer camps. It is hypothesized that archaeological sites tend to lose their cultural identity and specific cultural affiliation as the elevation of the site increases. Let x be the elevation (in thousands of feet) of an archaeological site in the southwestern United States. Let y be the percentage of unidentified artifacts (no specific cultural affiliation) at a given elevation. The following data were obtained for a collection of archaeological sites in New Mexico. 5.19 5.65 6.25 6.75 7.25 20 13 33 37 62 Complete parts (a) through (e), given Ex 31.09, Ey- 165, Ex-196.0461, Ey-6871, Exy 1082.75, and r 0.910. (a) Draw a scatter diagram displaying the data. Tools Actions CH 1. Select an object from the Tools menu to the left. Delte 2. Enter coordinates in Object Properties below, or use the mouse to place and move objects. To enter a fractional or decimal coordinate, use Object Properties. No. Soldion View our tutorial videos 7 Object Properties Tok r Cbd Selet MHelp WebAssign graphing tool (b) Verify the given sums Ex, Ey, E, Ey, Exy, and the value of the sample correlation coefficient r. (Round your value for r to three decimal places.) ΣΥ- Exy- (c) Find x, and y. Then find the equation of the least-squares line-a+bx. (Round your answers forx and y to two decimal places. Round your answers for a and b to three decimal places.) e cure to alet the noint (v u as a noint on the line ) Graph the least-squares line. Be sure to plot the point (x, y) as a point on the line. y 200r 200 150 150 100 100 50 50 0 2 3 4 5 6 7 1 2 3 4 5 6 7 -50 50 -100 -100 O-150 o-150 y 200 200 150 150 100 100F 50 50 0 1 2 5 6 7 1 2 4 5 6 7- -50E -50 -100 -100 o-150 -150 the coofficiont dotorn (e) Find the value of the coefficient of determination . What percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line? What percentage is unexplained? (Round your answer for to three decimal places. Round your answers for the percentages to one decimal place.) explained unexplained (f) At an archaeological site with elevation 6.1 (thousand feet), what does the least-squares equation forecast for y-percentage of culturally unidentified artifacts? (Round your answer to two decimal places.) %

Answer 1

(x-X) (y-y (x-x)(y-) Y S.No 5.19 13.3640 20 1.0568 169.0000 5.65 13 0.3226 400.0000 11.3600 6.25 33 0.0010 0.0000 0.0000 A 37 6.75 0.2830 16.0000 2.1280 67 5 7.25 1.0650 841.0000 29.9280 Total 2.7285 56,7800 31.09 165 1426,0000 70 6.2180 33.0000 SSY Mean SSX SXY 60 5 sample size: n= here 33.0000 6.2180 40 from above '2(x-X) 2.7285 Sa 30 20 2(X-X)(Y-)= Sy 56.7800 10 Sy/S slope B 20,81012 = C -BR= intercept -96.39733 hence line equation: -96.397 20.810 x correlation coefficient r 0.9103

b)

$\sum$x =31.09

$\sum$ y =165

$\sum$x² =196.0461

$\sum$y² =6871

$\sum$xy =1082.75

r =0.910

c)

xbar =6.22

ybar =33.00

yhat =-96.397+20.810x

d) bottom left curve is correct

e)

r² =0.829

explained =82.9%

unexplained =17.1%

f)

predicted value =-96.397+20.810*6.1 =30.54