00:01
In this question we are provided here a data table in the terms of ages, age and cholesterol level in age.
00:13
So first of all, to solve a question, we have to look at data table.
00:17
So here is the table.
00:18
Here we have placed age which is 59, 69, 43 and so on.
00:23
Calistrol levels are in the second row.
00:27
So now our first solution of the question will be we have to find our value for both.
00:34
Bar x sample mean so that is 1 upon x submission of x i which will be equal to 1 upon 10 sum of all values i is equal to 1 to 10 of x i and our value will be equal to 51 .2 similarly we will find here value for submission of i is equal to 1 to 10 x i coel square so here's the value and we have to just put them into the square and that is equal to 28 .110.
01:13
Then after we will find our value for i is equal to 1 to 10 for x i y i is equal to when we calculate by using excel we will get 98307 and then values for y will be as y bar which will be equal to 189 .6.
01:34
Summission of y i squared is equal to 364 -280.
01:43
So we will find our sum of square sum of xx is equal to summation of i is equal to 1 to 10.
01:50
For x i .2 .10 x bar square which is equal to 1845 .6 sum of y y is equal to summation of i is equal to 1 to 10.
02:09
For y i square minus 10 y square which is equal to y bar square i'm sorry which is equal to 4798 .4 so therefore value of s xy which is equal to as for formula i is equal to 1 to 10 x i by i which has to be subtracted by 10 times of y bar x bar and that is equal to to 1231 .8.
02:44
So here we are getting our values and now we can find our mean square error mean square error by using a formula 1 minus r squared s y divided by n minus 2 which is 10 minus 2 over here so that is equal to 499 .759 and therefore our value for r will be equal to s xy divided by a square root of s xy s y y and that will be calculated as 0 .408 4 so now our beta 1 cap for the correlation is s xy divided by s x x which is equal to 0 .698 i have calculated these values by using excel formulas.
03:47
So therefore we can set her null hypothesis as h -o is to beta 1 is equal to 0 and alternative hypothesis as h1 is to beta 1 which is not equal to 0.
04:08
So here we have taken where beta 1 is equal to true slope so as per the test statics test statics t is equal to beta 1 cap divided by s 8 multiplied by beta 1 cap so we can put our direct pally's over here 0 .6498 divided by 0 .5135 and that is equal to 1 .266 and beta 1 cap is equal to square root of mean square error divided by s x xxx.
04:57
And this time this is equal to 0 .5135 beta 1 cap.
05:04
So we are having our beta 1 cap value also and then after our p value and this is a two tail test so this implies us as 2p t is greater than 1 .266 t at 8 so we will get here 2 multiplied by 0 .12 0 .06 and therefore 0 .241 is greater than level of significance which is 0 .5 alpha...