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equation of the trend line

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The average SAT verbal score for students from one high school over the last ten exams is

508, 490, 502, 505, 493, 506, 492, 490, 503, 501

Write the equation of the trend line. Do the scores support an increasing or a decreasing trend?

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The expert depicts an equation of the trend line for verbal SAT scores.

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Equation Trends
The average SAT verbal score for students from one high school over the last ten exams is

508, 490, 502, 505, 493, 506, 492, 490, 503, 501

Write the equation of the trend line. Do the scores support an increasing or a decreasing trend? Please explain so I can fully understand/comprehend.
Solution. We can label the scores from the first to the tenth as follows.
X: the time the exam was taken;
Y: the score.

The i-th exam (X) the ...

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  • BSc , Wuhan Univ. China
  • MA, Shandong Univ.
Recent Feedback
  • "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
  • "excellent work"
  • "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
  • "Thank you"
  • "Thank you very much for your valuable time and assistance!"
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