Prueba cada modelo con dos o tres puntos de la tabla.
Trampas habituales
Interpretar la pendiente como si fuera el valor inicial.
Ejemplo resuelto
Recta de ajuste $y=3x+2$: para $x=4$ predice 14. Si el valor real es 15, el residuo es $15-14=1$.
Preguntas de ejemplo
Intenta responder antes de abrir la solución. Las preguntas están en el idioma del examen.
Pregunta 1
Dificultad fácil≈ 2 min
$x$
0
1
2
3
$y$
5
10
20
40
The table shows four values of $x$ and the corresponding values of $y$. Which equation best models the relationship between $x$ and $y$?
AA. $y=5x+5$
BB. $y=5x2$
CC. $y=2(5)x$
DD. $y=5(2)x$
Ver respuesta y explicación
Respuesta correcta: D. $y=5(2)x$
Explicación
Each time $x$ increases by 1, $y$ doubles $(5, 10, 20, 40)$, which is exponential growth with factor 2 and starting value 5 at $x=0$: $y=5(2)x$.
$y=5x+5$ fits only the first two points (it gives 15 at $x=2$). $y=5x2$ gives 0 at $x=0$. $y=2(5)x$ gives 2 at $x=0$.
Pregunta 2
Dificultad media≈ 1 min
Which of the following equations best models the data in the scatterplot?
AA. $y=1.5x+40$
BB. $y=-1.5x+40$
CC. $y=-1.5x+10$
DD. $y=-0.2x+40$
Ver respuesta y explicación
Respuesta correcta: B. $y=-1.5x+40$
Explicación
The points fall from left to right, so the slope is negative. Moving from about $(2, 37)$ to $(20, 11)$, $y$ decreases about $26$ while $x$ increases $18$, a slope of about $-1.4$. Extending the trend back to $x=0$ gives a $y$-intercept near $40$. So $y=-1.5x+40$ fits best.
$y=1.5x+40$ rises instead of falling. $y=-1.5x+10$ has a $y$-intercept far below the data. $y=-0.2x+40$ is much too flat: at $x=20$ it gives $36$, not about $11$.
Pregunta 3
Dificultad difícil≈ 2 min
Elevation, $x$ (hundreds of meters)
Mean July temperature, $y$ (°C)
$2$
$30.4$
$5$
$27.1$
$8$
$26.5$
$12$
$22.9$
$15$
$22.6$
The table shows the elevation $x$, in hundreds of meters, and the mean July temperature $y$, in degrees Celsius, at $5$ weather stations. A line of best fit for the data is $y=-0.6x+31$. For how many of the $5$ stations is the actual mean July temperature greater than the temperature predicted by the line of best fit?
AA. $1$
BB. $2$
CC. $3$
DD. $4$
Ver respuesta y explicación
Respuesta correcta: C. $3$
Explicación
Compute each prediction with $y=-0.6x+31$ and compare it with the actual value: $x=2$: $29.8$ (actual $30.4$, greater); $x=5$: $28$ (actual $27.1$, less); $x=8$: $26.2$ (actual $26.5$, greater); $x=12$: $23.8$ (actual $22.9$, less); $x=15$: $22$ (actual $22.6$, greater).
So $3$ stations are above the line. Choosing $2$ usually means missing the small difference at $x=8$; the stations at $x=5$ and $x=12$ are below the line, so the answer cannot be $4$.