Problem 3 Does how long children remain at the lunch table help predict how much

Question

Problem 3 Does how long children remain at the lunch table help predict how much they eat? The table gives data on 15 toddlers over several months at a nursery school. Time is the average number of minutes a child spent at the table when lunch was served. Calories is the average number of calories the child consumed during lunch, calculated from careful observation of what the child ate each day. Calories 472 465 456 423 437 50s 431 479 454 450 410 504 437 444 408 Time 21.4 37.7 33.5 32.8 39.5 22.8 34.1 33.9 43.8 42.4 43.1 29.2 31.3 33.0 43.7 Scatter Plot for Lunchtime Time min Figure 2: Scatter plot

Explanation / Answer

1. The linear regression equation is :

y^ = -2.9715X + 551.315

2. Correlation = .651
Time units of time if changed won't effect the correlation result

3. The R square will give you this. Therefore, 42.8% of the variation in Y is explained by X

4.If child spends 33.9 min then you have :450.118 calories

5.Residual at lunchtime 33.9 minutes us y^-y
= 450.119-479 = 29.119 min

6. Intercept is 551.315. Which means that if the time is 0 or the child doesn't spend anytime for lunch then he takes in calories of 551.315. Although, this non-intuitive it says that on an average w/o spending time for lunch children do take in some calories.

Slope is -2.9715. For an additional minute spend during lunch the child gets less of 2.97 calories

7. No. Since correlation is not causation we cannot say that more time spend lunching translates to lost of appetites.

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