Does how long children remain at the lunch table help predict how much they eat?

Question

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 speut 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. Scater Plot for Lunchtime Tmem Figure 2: Scatter plot Descriptive Statistics: Cov(Calories, Time)--135.0910 VariableNN Mean SE Mean StDev Minimum calories 15 0 451.87 7.76 30.07 408.00 431.00 450.00 472.00 508.00 Time 01 Median 03 Maximum 15 0 34.811.82 7.0421.40 31.30 33.90 42.40 43.80 i what is the regression line equation? [regression line: y=a+pr! 2. What is the correlation coefficient? If we recorded time at the table in hours rather than in minutes, how would the correlation change? properties of correlation coefficient 3. What fraction of variation of Calories is accounted for by lunchtime? (cocfficient of determination 4. What is the predicted calories the child consumes given that the child spends at the table for 33.9 minutes? Make prediction: given a particular value of predictor variable, find out the prediction value of the response variable. 5. What's the residual for the case of lunchtime 33.9 minutes? [Analysis of residual: Residual Actual Predicted 6. Explain the meaning of intercept and slope. 7. One analyst concluded that "it is clear from this correlation that toddlers who spend more time at the table eat less. Evidently something abont being at the table causes them to lose their appetites." Is this conclusion appropriate or not Keep in mind that Correlation is NOT Causation!

Explanation / Answer

Using R

> Calories=c(472,465,456,423,437,508,431,479,454,450,410,504,437,444,408)

> Time=c(21.4,37.7,33.5,32.8,39.5,22.8,34.1,33.9,43.8,42.4,43.1,29.2,31.3,33,43.7)
>
1) Regression line
> model=lm(Calories~Time)
> model

Call:
lm(formula = Calories ~ Time)

Coefficients:
(Intercept) Time  
546.636 -2.722  

so the regression line is given by

Calories=546.636 - 2.722 *Time

2) Correlation coefficint.

> cor(Calories,Time)
[1] -0.6377636

3)Coeeficient of determination
> R_square=summary(model)$r.squared
> R_square
[1] 0.4067425
40% variation expained by the response variable (Calories) to the regressor (Time).

4) Prediction when time =33.9

Calories=546.636 - 2.722 *Time

=546.636 - 2.722 *33.9

=454.3602

So the predicted calories is 454.36

Note - We will give you only 4-bit solution because of chegg rule .

>>>>>>>>>>>>>>>>>>>>>>>>>>>Best of luck <<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<

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