Test 2 Review
1.
The Following ordered pair data describes the grams of fat in a meal and the number of
calories.
r = 0.859
Variable
Formulas
a)
b)
c)
d)
e)
f)
Se = 32.2
Mean
StDev
Fat
9.428
15.2
Calories
170.44
60.46
y= a + bx
b = r
sy
sx
a= y − bx
Use the above information to write a regression line.
Write a sentence interpreting the meaning of the slope for the meal.
Write a sentence interpreting the meaning of the y-intercept for the meal.
Write a sentence interpreting the meaning of r2 for the meal.
Write a sentence interpreting the meaning of Se
Predict the number of calories in a meal with 37 grams of fat.
2. We looked at the at 40 randomly selected men to analyze the relationship between the
weight of a man and his BMI (Body Mass Index) and found the following graphs and
statistics:
R=0.800
BMI= 8.02 + 0.104Weight
a) What does the scatterplot tells us about the relationship between the weight and BMI?
b) A trainer said that if a man is heavy, it will cause him to have a large BMI. Does the
data support this statement?
c) What does r2 tell us?
d) Use the regression equation when appropriate to predict the weight of a men that are
220 lbs, and 100 lbs.
3. For the following ordered pairs, the least squares regression equation is 𝑦� = 3 + 2𝑥 Make a
scatter plot of the ordered pairs and draw the regression line on the scatterplot.
𝑆𝑆𝑆
Calculate the standard error using the formula 𝑠𝑒 = �𝑛−2 where n is the number of ordered
pairs (Round your values two the nearest hundredth).
x
1
2
3
4
5
6
7
8
y Predicted value 𝑦� Error (Residual) (𝐸𝐸𝐸𝐸𝐸)2
4
8
11
11
9
12
15
15
4. Find the percent increase or decrease for each of the following:
a)𝑦=2000(1.12)x
b) y=2000(1.03)x
c)𝑦=2000(1.003)x
e) 𝑦=2000(.956)x
f) 𝑦=2000(.12)x
d) y=2000(.82)x
3. The initial number of bacteria in a sample is 150,000 and it grows at a rate of 2% every day.
a. Write an exponential equation for the number of bacteria after t days.
b. Use your equation to predict the number of bacteria after 15 days.
5. A group of scientists observed a population of birds in a remote area and counted the birds in
1998. After returning every year and counting the birds, they came up with the following
formula for the number of birds: 𝑦=12000×(.84)t.
a) How many birds used to live in the area in 1998?
b) Predict the population in 2010.
6. A researcher has collected data on the price of gasoline from 1992 to 2014 and has found that
the price in dollars after t years can be predicted using the equation: y = − 0.0256t2 +.3584t
+1.90
a) According to this model what was the price of gas in1990?
b) Using this model predict the price of gas 1998?
c) Based on the equation, what year had the most expensive gas?
d) How much did gas cost in that year?
7. The bone mass in the average person’s legs decreases by 0.4 % every year. A person’s bone
mass is currently 8 kg.
a) Write an exponential equation for the mass after t years
b) Use our equation to predict the mass after 10 years.