20 medium SAT Two-variable data: models & scatterplots questions

The scatterplot shows the relationship between the number of hours studied, x, and test scores, y, for 10 students. The line of best fit for the data passes through approximately (2, 68) and (6, 84). For a student who studied 5 hours, the actual test score was 78. What is the sign of the residual for this data point?

• APositive, because the actual score is above the predicted score
• BNegative, because the actual score is below the predicted score
• CPositive, because 78 is greater than 5
• DNegative, because the line has negative slope in this region

The scatterplot shows the relationship between two variables, x and y. The scatterplot has 12 data points in a linear pattern trending down from left to right. A line of best fit passes through the approximate coordinates (3, 45) and (11, 21). Which of the following equations best represents the line of best fit?

• A$y = 54 - 3x$
• B$y = 54 + 3x$
• C$y = 21 - 3x$
• D$y = 45 - 8x$

According to the line of best fit, what is the meaning of the slope in this context?

• AThe predicted test score for a student who studies 0 hours per week
• BThe predicted increase in test score for each additional hour studied per week
• CThe predicted decrease in test score for each additional hour studied per week
• DThe maximum possible test score for students in the data set

The table shows the temperature T, in degrees Celsius, of a cooling liquid at time t minutes after it was removed from heat. t | T 0 | 100 2 | 61 4 | 37 6 | 23 8 | 14 Which of the following equations best models the relationship between t and T?

• A$T = 100 - 11t$
• B$T = 10 + 90(0.78^{t})$
• C$T = 100(0.5^{t})$
• D$T = -t^{2} + 100$

The scatterplot shows the relationship between study hours per week and test scores for a group of students. A line of best fit is also shown. At $x = 12$, which of the following is closest to the y-value predicted by the line of best fit?

• A$74$
• B$80$
• C$12$
• D$94$

The scatterplot shows the relationship between two variables, x and y. The scatterplot has 9 data points in a linear pattern trending upward from left to right. A line of best fit is shown passing through approximately (2, 15) and (10, 47). The data points range from $x = 1$ to $x = 11$. At $x = 6$, which of the following is closest to the y-value predicted by the line of best fit?

• A$27$
• B$31$
• C$6$
• D$55$

The scatterplot shows the relationship between two variables, x and y. A line of best fit for the data is also shown. Which of the following best interprets the slope of the line of best fit in context?

• AFor every increase of 1 thousand dollars in advertising spending, revenue increases by 7 thousand dollars.
• BFor every increase of 1 thousand dollars in advertising spending, revenue increases by 8 thousand dollars.
• CFor every increase of 1 thousand dollars in advertising spending, revenue increases by 26 thousand dollars.
• DFor every increase of 1 thousand dollars in advertising spending, revenue increases by 56 thousand dollars.

The table shows several values of x and their corresponding values of y. x | y 1 | 3 2 | 6 3 | 12 4 | 24 5 | 48 Which of the following equations best models the relationship between x and y?

• A$y = 3x$
• B$y = 1.5(2^{x})$
• C$y = 3x^{2}$
• D$y = 6x - 3$

The scatterplot shows the relationship between hours studied and test score for 10 students. A line of best fit is also shown. At $x = 5$, which of the following is closest to the test score predicted by the line of best fit?

• A$72$
• B$76$
• C$68$
• D$92$

Based on the line of best fit, what is the predicted average temperature, in degrees Celsius, for an elevation of 700 meters above sea level?

• A$14$
• B$17$
• C$20$
• D$8$

According to the model, what is the predicted increase in daily revenue, in dollars, for each additional hour the coffee shop is open?

• A$120$
• B$340$
• C$460$
• D$680$

The table shows the distance d, in feet, traveled by a car t seconds after the brakes were applied. t | d 0 | 0 1 | 19 2 | 36 3 | 51 4 | 64 Which of the following equations best models the relationship between t and d?

• A$d = 20t - t^{2}$
• B$d = 16t$
• C$d = 10(1.8^{t})$
• D$d = 25t - 2t^{2}$

The scatterplot shows the relationship between elevation and average temperature. A line of best fit is also shown. Based on the line of best fit, what is the predicted decrease in average temperature, in degrees Celsius, for each 1 hundred meter increase in elevation?

• A$8$
• B$2$
• C$0.5$
• D$1$

The scatterplot shows the relationship between altitude and temperature for 12 weather stations. A line of best fit is also shown. Based on the line of best fit, what is the predicted decrease in temperature, in degrees Fahrenheit, for each increase of 1 thousand feet in altitude?

• A$3$
• B$6$
• C$18$
• D$9$

According to the model, what is the predicted height of the plant, in centimeters, at the time of planting?

• A$2.5$
• B$5$
• C$8$
• D$10.5$

The table shows the profit P, in thousands of dollars, for a company in year t, where $t = 0$ corresponds to 2015. t | P 0 | 50 1 | 58 2 | 74 3 | 98 4 | 130 Which of the following equations best models the relationship between t and P?

• A$P = 50 + 20t$
• B$P = 50(1.3^{t})$
• C$P = 50 + 4t^{2} + 4t$
• D$P = 50 + 8t^{2}$

The scatterplot shows the relationship between temperature and ice cream sales. A line of best fit is also shown. Based on the line of best fit, what is the predicted increase in ice cream sales, in dollars, for each 1 degree Celsius increase in temperature?

• A$5$
• B$20$
• C$10$
• D$15$

The scatterplot shows the relationship between two variables, x and y. The scatterplot has 9 data points roughly along a line with positive slope. The line of best fit passes through approximately (2, 15) and (10, 47). At $x = 6$, which of the following is closest to the y-value predicted by the line of best fit?

• A$35$
• B$31$
• C$6$
• D$55$

Based on the line of best fit, what is the predicted reaction time, in milliseconds, for a participant who sleeps 7 hours per night?

• A$290$
• B$315$
• C$340$
• D$255$

According to the line of best fit, what is the predicted rental price, in hundreds of dollars per month, for an apartment located 11 kilometers from the city center?

• A$14$
• B$17$
• C$20$
• D$10$