rob is investigating the effects of font size on the number of words that fit on a page. he changes the font…

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.\nwords per page\n| font size | 14 | 12 | 16 | 10 | 12 | 14 | 16 | 18 | 24 | 22 |\n| word count | 352 | 461 | 340 | 407 | 435 | 381 | 280 | 201 | 138 | 114 |\nwhich 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?\n$y=-55x + 407$\n$y=-41x + 814$\n$y=-38x + 922$\n$y=-26x + 723$

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.\nwords per page\n| font size | 14 | 12 | 16 | 10 | 12 | 14 | 16 | 18 | 24 | 22 |\n| word count | 352 | 461 | 340 | 407 | 435 | 381 | 280 | 201 | 138 | 114 |\nwhich 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?\n$y=-55x + 407$\n$y=-41x + 814$\n$y=-38x + 922$\n$y=-26x + 723$

Answer

Answer:

y = - 41x + 814

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 $y=-41x + 814$.