Algebra One Two-Variable Statistics

The data for the distance d, in miles, remaining for a train to travel to its destination t hours after it departs a station are shown in the scatter plot. Which of the following functions best fits the data?

• d(t) = 50t + 300

• d(t) = 50t

• d(t) = −50t + 300

• d(t) = −50t

Emile collects data about the amount of oil A, in gallons, used to heat his house per month for 5 months and the average monthly temperature t, in degrees Fahrenheit, for those months. The scatter plot shows the data. The function A(t) = −1.4t + 96 best fits these data. Use A(t) to determine which of the following statements are true.

• Emile would use about 82 gallons of oil to heat his house for a month with average temperature 10 °F

• Emile would use about 85 gallons of oil to heat his house for a month with average temperature 15 °F.

• Emile would use 0 gallons of oil to heat his house for a month with average temperature 70 °F.

• Emile would use about 5 gallons of oil to heat his house for a month with average temperature 55 °F.

• Emile would use 96 gallons of oil to heat his house for a month with average temperature 0 °F.

The table shows the median weight, in pounds, of babies born at a particular hospital for the

first 6 months after they are born. The line y = 1.7x + 8.1 is fit to the data in the table,

resulting in the residual plot below. Which of the following are true?

• The residuals do not appear to follow a pattern.

• The residuals are mostly below the x-axis.

• The residuals are relatively small compared to the data values.

• The residuals are relatively large compared to the data values.

• The line is a good fit to the data.

The plot shows the residuals when a line is fit to a set of data. Based on the residual plot,

which statement best describes how well the line fits the data?

• The line is a good fit because the residuals are all close to the x-axis and are randomly distributed about the x-axis.

• The line is not a good fit because the residuals are not all close to the x-axis.

• The line is not a good fit because the residuals are not randomly distributed about the x-axis.

• The line is not a good fit because the residuals are not all close to the x-axis and are not randomly distributed about the x-axis.

The scatter plot shown suggests the association between the values of x with the values of y is linear. What is the y-intercept, rounded to two decimal places, of the linear function that represents the line of best fit?

• −1.96

• 11.15

• 11.41

• 22.36

The scatter plot shows the relationship between the time t, in years after 1900, and the life expectancy L, in years, at birth for a certain country. Do the data on the scatter plot suggest a linear association? If so, what is a function that represents the line of best fit?

• Yes; L(t) = 39.67t + 0.37

• Yes; L(t) = −0.24t + 74.33

• Yes; L(t) = 0.37t + 39.67

• No; the data on the scatter plot do not suggest a linear association.

The relationship between the amount of data downloaded d, in megabytes, and the time t,

in seconds, after the download started is shown. The data points on the scatter plot suggest

a linear association. Which of the following statements are true?

• The function that represents the line of best fit is approximately d(t) = 1.04t + 0.51.

• The data points on the scatter plot suggest a positive correlation.

• For every second that passes, about 1 additional megabyte is downloaded.

• For every second that passes, about 0.5 additional megabyte is downloaded.

• The function that represents the line of best fit is approximately d(t) = 0.51t − 1.04.

The linear equation c = 0.1998s + 76.4520 models the number of calories c in a beef hot dog as a function of the amount of sodium s, in milligrams, in the hot dog. What is the slope, and what does it mean in this context?

• The slope is 0.1998. The number of calories is increased by 0.1998 for each 1 milligram increase in sodium.

• The slope is 0.1998. The amount of sodium, in milligrams, is increased by 0.1699 for each increase of 1 calorie.

• The slope is 76.4520. This is the number of calories in a beef hot dog with no sodium.

• The slope is 76.4520. This is the amount of sodium, in milligrams, in a beef hot dog with no calories.

The linear equation c = 6.5n + 1500 models cost c, in dollars, to produce n toys at a toy factory. What is the c-intercept, and what does it mean in this context?

• The c-intercept is 6.5. The cost increases by $6.50 for each toy produced.

• The c-intercept is 6.5. The number of toys produced increases by about 6.5 for each $1 increase in cost.

• The c-intercept is 1500. It costs $1500 to run the factory if no toys are produced.

• The c-intercept is 1500. The factory can produce 1500 toys at no cost.

Which of the following correlation coefficients indicate a strong linear correlation?

• −0.872691

• −0.658799

• −0.125866

• 0.989862

• 0.798264