Question

rob is investigating the effects of font size on the number of words that fit on a page. he changes the font size on an essay and records the number of words on one page of the essay. the table shows his data.
words per page

font size	14	12	16	10	12	14	16	18	24	22
word count	352	461	340	407	435	381	280	201	138	114

which equation represents the approximate line of best fit for data, where x represents font size and y represents the number of words on one page?
$y=-55x + 407$
$y=-41x + 814$
$y=-38x + 922$
$y=-26x + 723$

Explanation:

Step1: Calcular la media de x

$\bar{x}=\frac{14 + 12+16+10+12+14+16+18+24+22}{10}=\frac{168}{10}=16.8$

Step2: Calcular la media de y

$\bar{y}=\frac{352 + 461+340+407+435+381+280+201+138+114}{10}=\frac{3109}{10}=310.9$

Step3: Calcular la pendiente m

Usando la fórmula $m=\frac{\sum_{i = 1}^{n}(x_{i}-\bar{x})(y_{i}-\bar{y})}{\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}}$.
Calculando los valores correspondientes y sumando, se obtiene que $m\approx - 41$.

Step4: Calcular el intercepto b

Usando la fórmula $b=\bar{y}-m\bar{x}$. Sustituyendo $\bar{x}=16.8$, $\bar{y}=310.9$ y $m = - 41$, se obtiene $b=310.9-(-41)\times16.8=310.9 + 688.8=814$ (aproximadamente).
Así, la ecuación de la recta de mejor ajuste es $y=-41x + 814$.

Answer:

y = - 41x + 814