Mathematics, 15.07.2019 00:40 destinyshanece08
For science class, a student recorded the high and low temperatures, in fahrenheit, over a ten day period in september. the data is shown in the table. a) what is the correlation for a linear model of this data? round to the nearest hundredth. r = b) ten high and low temperatures in october are recorded and have a correlation coefficient of 0.89. in which month is there a stronger correlation between the high and low temperatures? explain your answer.
Answers: 1
![r= \frac{n(\Sigma xy)-(\Sigma x)(\Sigma y)}{\sqrt{[n\Sigma x^2-(\Sigma x)^2][n\Sigma y^2-(\Sigma y)^2]}}](/tpl/images/0090/5812/c6d99.png)
![\begin{tabular} {|c|c|c|c|c|} x&y&xy&x^2&y^2\\[1ex] 26&49&1,274&676&2,401\\ 28&50&1,400&784&2,500\\ 30&57&1,710&900&3,249\\ 32&54&1,728&1,024&2,916\\ 34&60&2,040&1,156&3,600\\ 35&58&2,030&1,225&3,364\\ 37&64&2,368&1,369&4,096\\ 38&66&2,508&1,444&4,356\\ 41&63&2,583&1,681&3,969\\ 45&72&3,240&2,025&5,184\\[1ex] \Sigma x=346&\Sigma y=593&\Sigma xy=20881&\Sigma x^2=12284&\Sigma y^2=35635 \end{tabular}](/tpl/images/0090/5812/4614e.png)
![r= \frac{10(20,881)-(346)(593)}{\sqrt{[10(12,284)-(346)^2][10(35,635)-(593)^2]}} \\ \\ = \frac{208,810-205,178}{\sqrt{(122,840-119716)(356,350-351,649)}} = \frac{3,632}{\sqrt{(3,124)(4,701)}} \\ \\ = \frac{3,632}{\sqrt{14,685,924}} = \frac{3,632}{3,832.22} =\bold{0.95}](/tpl/images/0090/5812/12e4b.png)
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