Question

read the following description of a data set.
a food scientist wants to understand how much sugar children like in their desserts. he sets up a study where children taste cups of vanilla pudding with varying sweetness and rate each cup on a scale of 1 to 10, where 10 is excellent.
for each tasting, the food scientist writes down the grams of sugar in the pudding cup, x, as well as its rating, y.
the least squares regression line of this data set is:
y = 2.356x - 40.511
what rating does this line predict for a pudding cup with 24 grams of sugar?
round your answer to the nearest integer.

Explanation:

Step1: Sustituir el valor de \(x\) en la ecuación

Dado \(x = 24\) y la ecuación \(y=2.356x - 40.511\), sustituimos \(x\):
\(y=2.356\times24 - 40.511\)

Step2: Calcular el primer término

Calculamos \(2.356\times24\):
\(2.356\times24 = 56.544\)

Step3: Calcular el valor de \(y\)

Sustituimos el resultado del paso 2 en la ecuación:
\(y = 56.544-40.511\)
\(y=16.033\)

Step4: Redondear al entero más cercano

Redondeamos \(16.033\) al entero más cercano. Como \(0.033<0.5\), redondeamos hacia abajo.

Answer:

\(16\)