Regression Models Assignment and Quiz 90%

The table below shows the height of a ball x seconds after being kicked. What values, rounded to the nearest whole number, complete the quadratic regression equation that models the data? f(x) = x2 + x + 0 Based on the regression equation and rounded to the nearest whole number, what is the estimated height after 0.25 seconds? feet

-16 81 19

The table below shows the population of a town over x years. What values, rounded to the nearest tenth, complete the exponential regression equation that models the data? f(x) = ()x Based on the regression equation and rounded to the nearest whole person, what is the estimated population after 25 years? people

10346.0 1.1 112096

The data in the table compares x, the number of pages in a chapter, to y, the amount of time, in minutes, spent reading. The function y = 0.86x - 0.09 models the data in the table. Which is the best prediction for the number of pages in a chapter that takes 18 minutes to read? 15 17 19 21

21

The table shows the wavelength of the sound produced by keys on a piano x keys away from the A above middle C. Using the exponential regression model, which is the best prediction of the wavelength of the key that is 8 above the A above middle C? 49.31 cm 49.44 cm 49.73 cm 49.78 cm

49.44 cm

A professor uses a video camera to record the motion of an object falling from a height of 250 meters. The function f(x) = -5x2 + 250 can be used to represent the approximate height of the object off the ground after x seconds. Which is the best estimate for the amount of time elapsed when the object is 120 meters off the ground? 4 seconds 5 seconds 6 seconds 7 seconds

5 seconds

Marta's mother shared a funny video of their cat on the Internet. The total number of people who had viewed the video over the first 30 days could be modeled using the function f(x) = 33(1.3)x where x is the number of days the video has been online. About how many people had viewed the video once it had been online for 20 days? 190 858 6,271 86,460

6,271

Galton attempted to mathematize the work done by his famous cousin ______. Galton's study enlisted the help of his friends to grow ______. His study lead to the mathematical notion of _____.

Darwin sweet peas regression

The quadratic regression graphed on the coordinate grid represents the height of a road surface x meters from the center of the road. A graph shows the horizontal axis numbered negative 7 to positive 7 and the vertical axis numbered negative 1.25 to positive 1.25. A line shows an upward then downward trend. What does the graph of the regression model show? The height of the surface decreases from the center out to the sides of the road. The height of the surface increases, then decreases, from the center out to the sides of the road. The height of the surface increases from the center out to the sides of the road. The height of the surface remains the same the entire distance across the road.

NOT: The height of the surface increases, then decreases, from the center out to the sides of the road.

Explain the concept of regression to the mean between generations.

Regression to the mean is the phenomenon that occurs when the next generation, or offspring values, regresses to the overall mean of the population. Extreme traits are not increased or decreased in measure, but trend back to the average.

The table below shows the profit based on price for an object sold by a company. Which statements are true? Check all that apply. The data is best represented by an exponential model. The data is best represented by a quadratic model. If the price is $5 per unit, the expected profit is approximately $4,686. If the price is $80 per unit, the expected profit is negative. As the price per unit increases, the profit increases indefinitely.

The data is best represented by a quadratic model. If the price is $5 per unit, the expected profit is approximately $4,686.

The value of a car decreases as shown in the table below. A 2-column table with 6 rows. The first column is labeled years after purchase with entries 0, 1, 2, 3, 4, 5. The second column is labeled value (dollar sign) with entries 25,000; 18,000; 14,000; 10,500; 8,000; 6,000. Which statements are true? Check all that apply. The function that best represents the data is f(x) = 24,512(0.755)x. The function that best represents the data is f(x) = 554x2 - 5,439x + 24,600. The function decreases indefinitely. It is reasonable to interpolate to the value of the car at 4.5 years. It is reasonable to extrapolate to 40 years.

The function that best represents the data is f(x) = 24,512(0.755)x. The function decreases indefinitely. It is reasonable to interpolate to the value of the car at 4.5 years.

Jessica plots the data points relating the amount of money she needs to repay a loan and the number of months she has been making payments. She calculates two regression models. Which is true? The linear model better represents the situation because the amount she owes is decreasing by about the same amount every 6 months. The linear model better represents the situation because according to the exponential model, the repayment amount will never be 0. The exponential model better represents the situation because the amount she owes decreases by about the same amount every 6 months. The exponential model better represents the situation because according to the linear model, the repayment amount will eventually be negative.

The linear model better represents the situation because the amount she owes is decreasing by about the same amount every 6 months.

A farmer harvests apples that are heavier than the average 5 kg weight for that variety. He plants the seeds from the harvest hoping that the next generation will produce even heavier apples. Using the results found by Galton, which statement is most likely true regarding the weight of the next generation? The next generation will weigh twice as much as the parent generation, closer to 10 kg. The next generation will weigh exactly the same as the parent generation. The next generation will weigh less than the parent generation, closer to 5 kg. The next generation will weigh less than the parent generation, closer to 2.5 kg.

The next generation will weigh less than the parent generation, closer to 5 kg.

The graph shows the relationship between men's shoe sizes and their heights. What type of relationship is this? a linear relationship showing as height increases, shoes size increases a linear relationship showing as height increases, shoe size decreases a quadratic relationship showing as height increases, shoe size increases, then decreases a quadratic relationship showing as height increases, shoe size decreases, then increases

a linear relationship showing as height increases, shoes size increases

Mr. Valdez puts $10,000 in a retirement account and does not make any deposits or withdrawals. The table below shows the amount of money in the account after x years. What values, rounded to the nearest hundredth, complete the exponential regression equation that models the data?

f(x) = 9974.73(1.05)x

Use the drop-down menus to complete the statement about the volume of a water storage tank over time, as shown in the table. The data in the table can best be described as ______ because there is a _______.

exponential constant multiplicative rate of change

The table below shows the approximate height of a ball thrown up in the air after x seconds. Which quadratic model best represents the data? f(x) = -16x2 + 99x + 6 f(x) = -36x2 + 37x + 5 f(x) = 36x2 + 37x + 5 f(x) = 16x2 + 99x + 6

f(x) = -16x2 + 99x + 6

The table shows the relationship between time spent running and distance traveled. Which type of model best describes the relationship? linear, because the r value for the linear model is closest to 1 exponential, because the r value for the exponential model is closest to 0 linear, because the rate of change between each pair of points is exactly 520 exponential, because the rate of change between each pair of points is 1.98

linear, because the r value for the linear model is closest to 1

Which type of function best models the data shown on the scatterplot?

quadratic

What did Galton use to calculate how strong the relationship was for the line of best fit? a bell shaped curve forensics genetic testing the correlation coefficient

the correlation coefficient

The data in the table represents a company's profit based on the number of items produced. Which equation best represents the data? y = -1.026x2 + 1016.402x - 162075 y = -1.036x2 + 1024.771x - 163710 y = 298.214x - 66317.667 y = 196.2x - 18710

y = -1.026x^2 + 1016.402x - 162075

The table shows the estimated number of bees, y, in a hive x days after a pesticide is released near the hive. Which function best models the data? y = 9,958(0.972)x y = 0.972(9,958)x y = 9,219x- 150 y = -150x + 9,219

y = 9,958(0.972)x

The graph shows the data points in the table and the exponential regression model associated with the data. Based on the graph of the regression model, which is true? The number of weeds is decreasing by a multiplicative rate. The number of weeds is increasing by a multiplicative rate. The number of weeds is decreasing by an additive rate. The number of weeds is increasing by an additive rate.

The number of weeds is decreasing by a multiplicative rate.

Charlie used a regression calculator to generate the equation f(x) = -0.15x + 20.1 for the ordered pairs (2, 15), (4, 21), (6, 26), (8, 20), and (10, 14). Is a linear representation the best way to represent the data? If it is, explain why. If not, explain why and suggest a better alternative.

The r-value for the linear function related to the ordered pairs is very close to zero, so it is not a good representation of the data. A quadratic model would better represent the data because there is a turning point within the data set. The data increases then decreases, which is what the graph of a quadratic does.

The table represents the temperature of a cup of coffee over time. Which model best represents the data set? exponential, because there is a relatively consistent multiplicative rate of change exponential, because there is a relatively consistent additive rate of change linear, because there is a relatively consistent multiplicative rate of change linear, because there is a relatively consistent additive rate of change

exponential, because there is a relatively consistent multiplicative rate of change