Question

E D Correlation coefficient 0.9400279 المة 1800 Presidential Election Electoral Votes 25 20 15 A 1 State 2. CT 3 DE 4 GA 5 KY 6 MD 7 MA 8 NH 9 NJ 10 NY 11 NC 12 IPA 13 RI 14 SC 15 TN 16 VT 17 VA 18 B С Population(thousands) Electoral Votes 251 9 64 163 4 221 4 342 10 423 16 184 6 211 7 589 12 478 12 602 15 66 4 346 8 106 3 3 154 4 808 21 Electoral Votes . . 10 . . 5 0 0 100 200 300 SOO 700 800 900 400 600 State Population(thousands) Seriesi (346,8), (106,3) Slope= y2-y1/x2-x1 Slope= (3)-(8)/(106)-(346)= 1/48 y=1/48x+19/24 1. Use the regression equation to calculate the number of Electoral votes that a state with a population of 1,000,000 would have. Since our units of population are in thousands, substitute x=1000 into the formula, find the value of y and round to the nearest whole number (since it is measuring electoral votes). Do this in Excel using what you know about Excel formulas. 2. Is this meaningful as a state population? Why or why not? 3. Discuss, briefly, what the value of the correlation coefficient (and the scatter plot) reveals about the relationship between population and electoral votes. (in other words, is it a strong or weak correlation, and why?) 4. Many states did not exist in 1800. Find three states which had no electoral votes in 1800 and write down the first presidential election in which they voted. (You will probably need to look this up on the internet)

Answer 1

Question 1).

• Let y* be the predicted value of electoral votes
• Let x be the population (in thousand)

NOW,

A D E F 1 XY 81 9 2 3 4 5 16 6 7 B C Population (x) Electoral Votes (Y) X? Y2 251 9 63001 64 3 4096 163 4 26569 221 4 48841 342 10 116964 423 16 178929 184 6 33856 211 7 44521 589 12 346921 478 12 228484 602 15 362404 16 100 256 36 49 144 2259 192 652 884 3420 6768 11041 1477 7068 8 9 10 11 144 5736 12 225 9030 13 66 4 4356 16 264 14 346 8 64 2768) 119716 11236 15 106 3 9 318 16 154 4 23716 16 616 17 808 21 652864 441 16968 18 19 SUM: 5008 138 2266474 1622 59524

С. Equation couich is we to find have Regression аvеи ба ІІ. а " В. + p. x биец ро ві In }ечер. 8 slope о we find and ßi have to which are Bo given by о (37) 19- с. n (EN) - 3 x)

and B.Ex Bo carakaning and pulting values, we Now puiting have. Bi = 16(138 16(59594) BI (5008) (138) 16(2266474) - (5008)2 ßi 952384 691104 025636263584 - 25080064 ßi 261280 11183520 ßi 0.0234 Now ßo 138 - 0.0234) (5008) 16 11 138 117. 0016 po 16 Bo 20.9984 16 ßo 1:3194

Then fore Owl (-3)2ч + 0 •o23ч х regression Equation is ya given рата ression Equation 1-312ч + o- 023ч (ooo) Now у= looo we are that in regres 1. 312ч + 23. у 24,412 Ч 2S There fore тие ане 25 Electoral to a stale with voles correspond- po pulation. Тоооооо га