Fast food is often considered unhealthy because much of it...

Fast food is often considered unhealthy because much of it is high in both fat and calories. The following table gives relevant information about different food items with fat and calorie content. Fat Calories 19 410 31 580 34 590 35 570 39 640 39 680 43 660 A new burger containing 30 grams of fat is introduced. How many "predicted" calories does the burger have? How many predicted calories a burger containing 43 grams of fat would have? What would be the residual?

Transcript

00:01 Hey there, welcome to numerate.

00:03 So we are given a problem here where we ask to compare the fat in calories contents here and use one to protect the other.

00:16 So fat is x, calories is y, and we're asked to construct a regression equation.

00:21 So regression equation format is going to be y predictor equals bx, where b is the slope plus a where a is y intercept.

00:31 So let's figure out what's the sum of squares here.

00:36 Sum of squares equals the sum of x minus this means.

00:40 So i went ahead and calculated the means for both x and y.

00:43 So we had 34 .3 squared equals 365 .4.

00:59 And now for the sum of products, we're going to take the sum of x minus this mean.

01:07 34 .3 and multiplied by y minus this mean, which is 590.

01:16 This gives us a sum of products that equals around 4 ,040.

01:23 Now with this, we can use these two stats to find our slope.

01:29 Our slope here equals the sum of products that we found divided by the sum of squares of x.

01:39 Let's write a straight line over here, which equals around 11 .1.

01:56 Let's carry our digits here.

01:58 How many digits do we need? let's do three digits, 0 .56.

02:09 And for our 8 intercept, take a y mean minus a slope times our x mean, giving us an intercept of around 210 .954.

02:24 Therefore, our overall regression here is y predictor equals our slope 11 .056x plus our intercept 210 .954...

Question

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