Every few years, the National Assessment of Educational Progress asks a national sample of eighth-graders to perform the same math tasks. The goal is to get an honest picture of progress in math. Suppose these are the last few national mean scores, on a scale of 0 to 500.
Year 1990 1992 1996 2000 2003 2005 2008
Score 263 268 271 272 276 277 279
(a) Find the regression line of mean score on time step-by-step. First calculate the mean and standard deviation of each variable and their correlation (use a calculator with these functions). Then find the equation of the least-squares line from these
(b) What percent of the year-to-year variation in scores is explained by the linear trend?

a)X: 0  2   6  10  13  15  18

Y:263 268 271 272 276 277 279

X represent the number of years since 1990

n=7  

And in order to calculate the correlation coefficient we can use this formula:

And the slope would be:

Now we can find the means for x and y like this:

And we can find the intercept using this:

So the line would be given by:

b) For this case the percent of variation in scores is explained by the linear trend is given by the determination coefficient and we got:

So then we can say that the percent of variation explained is approximately 95.26%

Step-by-step explanation:

Pearson correlation coefficient(r), "measures a linear dependence between two variables (x and y). Its a parametric correlation test because it depends to the distribution of the data. And other assumption is that the variables x and y needs to follow a normal distribution".

Solution to the problem

Part a

We assume the following data:

X: 0  2   6  10  13  15  18

Y:263 268 271 272 276 277 279

X represent the number of years since 1990

n=7  

And in order to calculate the correlation coefficient we can use this formula:

So then the correlation coefficient would be r =0.976

The mean for X on this case is given by:

For this case we need to calculate the slope with the following formula:

Where:

So we can find the sums like this:

With these we can find the sums:

And the slope would be:

Now we can find the means for x and y like this:

And we can find the intercept using this:

So the line would be given by:

Part b

For this case the percent of variation in scores is explained by the linear trend is given by the determination coefficient and we got:

So then we can say that the percent of variation explained is approximately 95.26%

i dont know sorry

step-by-step explanation:

5x+10 is the correct one

hope this