Answer to Question #233784 in Statistics and Probability for Jesiel Alfanta

Question #233784

The following table gives the average monthly exchange rate between the U.S. dollar and the euro for 2009. It shows that 1 euro was equivalent to 1.324 U.S. dollars in January 2009. Develop a trend line that could be used to predict the exchange rate for 2010. Use this model to predict the exchange rate for January 2010 and February 2010.

MONTH EXCHANGE RATE


1
Expert's answer
2021-09-09T00:13:56-0400
"\\def\\arraystretch{1.5}\n \\begin{array}{c:c}\n x & y \\\\ \\hline\n 1 & 1.289 \\\\\n \\hdashline\n 2 & 1.324\\\\\n\\hdashline\n 3 & 1.321 \\\\\n \\hdashline\n 4 & 1.317\\\\\n\\hdashline\n 5 & 1.280 \\\\\n \\hdashline\n 6 & 1.254\\\\\n\\hdashline\n 7 & 1.230 \\\\\n \\hdashline\n 8 & 1.240\\\\\n\\hdashline\n 9 & 1.287 \\\\\n \\hdashline\n 10 & 1.298\\\\\n\\hdashline\n 11& 1.283 \\\\\n \\hdashline\n 12 & 1.311\\\\\n\n\\end{array}"

"\\bar{x}=\\dfrac{\\sum_ix_i}{n}=\\dfrac{78}{12}=6.5"

"\\bar{y}=\\dfrac{\\sum_iy_i}{n}=\\dfrac{15.434}{12}=1.286167"

"SS_{xx}=\\sum_ix_i^2-\\dfrac{1}{n}(\\sum_ix_1)^2=650-\\dfrac{1}{12}(78)^2"

"=143"

"SS_{yy}=\\sum_iy_i^2-\\dfrac{1}{n}(\\sum_iy_1)^2=19.861426-\\dfrac{1}{12}(15.434)^2"

"=0.010730"


"SS_{xy}=\\sum_ix_iy_i-\\dfrac{1}{n}(\\sum_ix_1)(\\sum_iy_i)"

"=100.03-\\dfrac{1}{12}(78)(15.434)=\u22120.291000"

"slope=m=\\dfrac{SS_{xy}}{SS_{xx}}=\\dfrac{\u22120.291000}{143}=-0.002"

"b=\\bar{y}-m\\cdot\\bar{x}=1.286167-(-0.002)(6.5)"

"=1.2994"

The equation of the trend line is


"y=-0.002x+1.2994"



January 2010


"y=-0.002(13)+1.2994"

"y=1.273"

February 2010


"y=-0.002(14)+1.2994"

"y=1.271"

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