Section II Sample Examination Five 251 5. The 28 students in a fourth-grade clas

Question

Section II Sample Examination Five 251 5. The 28 students in a fourth-grade class were to beach. The students were all taken a rocky given identical metal containers and were asked to collect as many as they wished. Once the activity was over, the pebbles of teacher recorded, for each student, the number collected the weight (y), to the nearest ounce, of the filled container. The results are pairs were the same. The equation of the least squares regression line is j 13.419 3.865x. 100 80 a 70 60 50 40 30 5 6 7 9 10 11 12 13 14 15 16 17 18 19 20 8 Number of Pebbles (a) Draw the least squares regression line on the scatterplot. (Note that the smallest value on the horizontal axis is 5, not 0. (b) One student collected 16 pebbles, and the weight of the filled container for this student was 82 ounces. Circle the point on the scatterplot represents this student's results and draw the line segment on the scatterplot that corresponds to the residual for this point. Give a numerical value of this residual.

Explanation / Answer

a) we canot plot this for you as data is not given

b)

we are given x = 16 and y = 82 , this is an observed value. Now lets calculate the predicted value based on the regression equation

yhat = 13.419 +3.865*x, so we put x = 16 and solve the value for yhat = 75.259

now residual is

actual value - predicted value

= 82-75.259

= 6.741

c)

This means that the model prediction value and the observed value differ by 6.74 units. Or the fitted regression line and the data point(16,82) are at a distance of 6.741 units

d)

yhat = 13.419 +3.865*x

we see that the slope is 3.865 . This means that for every additional value of pebble the value of weight changes by 3.865 units. This means if 1 pebble is added , then the weight is increased by 3.865 units

now if we put x = 0 in this regression equation

yhat = 13.419 +3.865*x , x = 0

we get yhat = 13.419 units , so this means that if there were no pebbles than the weight would be 13.419 units

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