The table shows g(k, t) weight gain/loss of a pig. + Average...

The table shows $g(k, t)$ weight gain/loss of a pig. + Average Daily Weight Gain/Loss for a Pig (kg/day) Air temp. (°C) Mean live weight (kg) 68 91 113 136 156 4.4 0.58 0.54 0.50 0.46 0.43 10.0 0.67 0.71 0.76 0.80 0.85 15.6 0.79 0.87 0.94 1.02 1.09 21.1 0.98 1.01 0.97 0.93 0.90 26.7 0.83 0.76 0.68 0.62 0.55 32.2 0.52 0.40 0.28 0.16 0.05 37.8 -0.09 -0.35 -0.62 -0.88 -1.15 (a) What is the average daily weight gain/loss for a 156-kg pig when the temperature is 26.7°C. kg/day (b) Find the function for the linear model that gives the average daily weight gain/loss of a pig in kg/day when the air temperature is 32.2°C, where $k$ is the pig's weight in kg, with data from $68 leq k leq 156$. (Round all numerical values to four decimal places.) g(k, 32.2) = kg/day (c) Find and interpret the rate of change of the average daily weight gain/loss of a pig when the air temperature is 32.2°C with respect to the pig's weight when the mean live weight is 113 kg. (Round your answers to four decimal places.) kg/day per kg A pig whose mean live weight is 113 kg when the air temperature is 32.2°C ---Select--- on average kg/day per kg.

Transcript

00:01 For part a, we know that we're looking for a 156 kilogram pig.

00:07 So if we look at the chart, we can see that we have the mean live weight, 156 kilograms, is the fifth column.

00:20 And we know that we have that the temperature is 26 .7 degrees celsius.

00:26 Looking at the chart given, 26 .7 degrees celsius is 1, 2, 3, 4, 5.

00:31 That is the fifth row.

00:32 So, the value that we want to give then would be, i'll call it x -55 for row 5 column 5, which is going to be, let's see here, that is 0 .55 kilograms per day.

01:00 Then, moving on to part b, what we'll want to do is essentially a simple linear regression, y -hat equals b -0 plus b -1 -x, where the different values for x are, really this would be k as it's dictated to us, the different values for k would be the pig's weight.

01:23 And this is the weight gain slash loss given weight at 32 .2 degrees celsius.

01:45 So we have that the slope of our regression line is going to be found by taking the sum of each k value, so each weight value minus the average of the weight values times each each each weight values, weight gain slash loss value y minus the average of the y values divided by the sum of k minus k bar squared now for the sake of making the calculations a little bit easy here i'm going to do this in excel all right so first thing that we want to do is find the average of k and y which we can do either by adding up all of the individual values so in this case we can see this sum is 565, then we take that and divide it by the number of cells, so 564, pardon me, 564 over 5, gives us the average, which is here 112 .8, and then similarly for y, we have the sum would be 1 .41, so the average is 0 .282.

02:50 Then we want to have a column for k minus k bar times y minus y bar.

02:57 Oops, not y bar, zero, y bar close parentheses.

03:01 And we also want to to have a column for k minus k bar squared.

03:09 So for k minus k bar times y minus y bar, the first value would be 68 minus 112 .8 times 0 .52 minus 0 .282.

03:20 So the first value would be negative 10 .6624.

03:24 And then for k minus k bar squared, that would first be 68 minus 112 .8 all squared.

03:30 Do that for each.

03:33 And then we'll want to sum up across each one of those columns.

03:43 So we then have, oh one second here that's left over from a previous problem, we then have that our slope b1 is going to be equal to negative 26 .088 divided by 4886 .8.

03:54 So the slope is roughly negative 0 .005...

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