They say that as you get older you need to take vitamins a...

They say that as you get older, you need to take vitamins. A researcher wanted to see if this was true and had adults of various ages record their amount of dairy intake in ounces to see if they need a vitamin supplement. Age 70 81 61 72 51 45 60 59 45 42 Dairy (ounces) 4 7 9 14 16 18 18 19 18 21 (a) Compute r. (Round your answer to three decimal places.)

Transcript

00:01 Hello students, according to the given question we have to find the correlation and regression values.

00:07 So here given x and y values so from that total n is equal to 8 summation x is equal to 396 summation y is equal to 1152 x bar is equal to 49 .5 y bar is equal to 144 and sum of squares of x is equal to 6292 and sum of squares of y is equal to 8644 sum of products is equal to minus 6897.

00:44 Now in the a bit we have to find the correlation r is equal to sum of products by square root of sum of squares of x into sum of squares of y that is equal to minus 6897 is divided by square root of 6292 into 8644.

01:07 So r is equal to minus 0 .9352.

01:12 In the b bit alpha is equal to 0 .1 and hypothesis h naught such that alpha rho is equal to 0 and h1 such that rho equal to 0.

01:27 So in this case for the first one t critical value is 2 .4469 because n is equal to 8 so degrees of freedom is n minus 2 is equal to 6 and for the second one t is equal to r into square root of n minus 2 divided by square root of 1 minus r square by substituting minus 0 .9352 into square root of 8 minus 1 8 minus 2 is divided by square root of 1 minus 0 .9352 square.

02:09 So then t value is equal to minus 6 .4689 here degrees of freedom is 6.

02:17 So in this case p value will be equal to 0 .00 which is less than alpha that is 0 .1.

02:26 So in this case we have to reject the null hypothesis h naught.

02:32 Now in the c bit slope b is equal to sum of products by sum of squares of x by substituting minus 6897 divided by 6292 is equal to minus 1 .096...

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