find the equation for the least squares regression line of the data described below. eduardo is indignant…
find the equation for the least squares regression line of the data described below. eduardo is indignant that his favorite author takes too long to write new books. to determine how atypical his favorite authors speed is, eduardo looked at how writing speed varies between different active authors. for his favorite novelists, he recorded the number of years they had been actively writing, x, and how many novels they had written, y.\nyears novels\n9 13\n20 13\n22 15\n22 13\n34 18\nround your answers to the nearest thousandth.\ny = x +
Answer
Explicación:
Paso 1: Calcular sumas necesarias
Sean $n = 5$, $x_i$ los valores de años y $y_i$ los valores de novelas. Calculamos $\sum_{i = 1}^{n}x_i=9 + 20+22 + 22+34=107$, $\sum_{i = 1}^{n}y_i=13 + 13+15+13+18=72$, $\sum_{i = 1}^{n}x_i^2=9^2 + 20^2+22^2 + 22^2+34^2=81+400+484+484+1156 = 2605$, $\sum_{i = 1}^{n}x_iy_i=9\times13 + 20\times13+22\times15+22\times13+34\times18=117+260+330+286+612 = 1605$.
Paso 2: Calcular la pendiente $m$
La fórmula para la pendiente $m$ de la línea de regresión es $m=\frac{n\sum_{i = 1}^{n}x_iy_i-\sum_{i = 1}^{n}x_i\sum_{i = 1}^{n}y_i}{n\sum_{i = 1}^{n}x_i^2 - (\sum_{i = 1}^{n}x_i)^2}$. Sustituyendo los valores: $m=\frac{5\times1605 - 107\times72}{5\times2605-(107)^2}=\frac{8025 - 7704}{13025 - 11449}=\frac{321}{1576}\approx0.204$.
Paso 3: Calcular la intersección $b$
La media de $x$ es $\bar{x}=\frac{\sum_{i = 1}^{n}x_i}{n}=\frac{107}{5} = 21.4$, y la media de $y$ es $\bar{y}=\frac{\sum_{i = 1}^{n}y_i}{n}=\frac{72}{5}=14.4$. Usando la fórmula $b=\bar{y}-m\bar{x}$, tenemos $b = 14.4-0.204\times21.4=14.4 - 4.366 = 10.034$.
Respuesta:
$y = 0.204x+10.034$