Answer to Question #160544 in Statistics and Probability for Elyn

Question

The following table shows the Final grade of ten students in Algebra and Statistics. Find out what

will be the student grade in Algebra if his grade in statistics is 100. Is there a significant

relationship between the grade in statistics and algebra? Interpret your result.

Algebra (x) 75 80 93 65 87 71 98 68 84 77

Statistics (y) 82 78 86 72 91 80 95 72 89 74

Answer 1

Solution:

1) We need to apply linear regression to the data to predict the value of the Algebra, given the value of statistics.

The prediction value is: $p(100) = 100.617$

and the curve equation is $ŷ = 1.15011X - 14.39389$

2) To find the significance between data, we need to find the p-value. In our case, we first find Pearson (R), it is equal to

$r = 0.8721$.

P-value is calculated from Pearson (R) using the t distribution which is:

$t = \frac{r\sqrt{n-2}}{\sqrt{1-r^2}}$

Then, t value is $2*P(T>t), where$ T follows a t distribution with n-2 degrees of freedom (number of samples). In our case, $p = .001$ , which means that results of the statistics are significant. So, there exists a connection between Statistics grade and Algebra grades. In our case, we can interpret that the Algebra Value indeed has connection to the Statistics value and the Algebra mark should be around 100 for the given student with the 100 mark for the statistics.