11. The following data represents the yield y of a chemical...

11. The following data represents the yield y of a chemical reaction at various temperatures x : x(F°) y 150 77.4 150 76.7 160 78.2 180 84.5 200 83.9 200 83.7 225 85.6 250 88.9 250 90.3 280 94.8 The summary statistics are: x? = 204.5, y? = 84.4, sx = 45.7, sy = 5.89, and r = 0.975. a. Find the equation of the regression line of y on x. b. What yield is predicted for the temperature x = 190? c. What is the residual associated with the observation (225, 85.6)? d. The yield is predicted to increase by ___________ for every 1° increase in temperature.

Transcript

00:01 Hi, i'm david and i'm here to help you answer your question.

00:04 Now let me bring up your question here.

00:06 In the question here we're going to reveal about the linear regression.

00:10 Let me remind you that the formula will be the y heart, it would equal to the b0 plus the p1 times from the x, where the b0 it would equal to the y bar minus the p1 times of the x bar.

00:24 The b1, there's a formula that relating the correlation coefficient here will be r times with the x bar.

00:30 S y over the x and in this question here we are given those information about the x by whereby the standard division as well as the r therefore we should be able to find the b1 so b1 equal to r which is the 0 .975 standard division of the y equal to the 5 .89 our standard division of the x point seven and then we get equal to the 0 .1 2 so we want to round to the 4 decimal places here 1 257 and when we get the b1 we can find the b0 it will equal to y power equal to 84 .4 minus b1 will be 0 .1 257 time with the x part 2 of 4 .5 then we get equal to the 804 4 .4 minus 0 .1257 times the answer, then with the answer times 2 .0 .5, get equal to the 58 point 7021.

01:58 Therefore the equation we have here going hot equal to the 58 point 7021 plus 0 .157 and then times with the x.

02:12 And that's going to be the answer for the a.

02:15 Now for the b, 125 if we have the x equal to 190 and then we do have the y heart, the prediction it will equal to the 508 point 0 .021 plus 0 .17.

02:31 X now equal to the 190...

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