1. Given the following regression equation for a line, would the sign of the correlation coefficient, r, be positive or negative? (3 points) Explain why. (3 points) y' = XXXXXXXXXX2x 2. Answer the...

1. Given the following regression equation for a line, would the sign of the co
elation coefficient, r, be positive or negative? (3 points) Explain why. (3 points)
y' = XXXXXXXXXX2x
2. Answer the following questions based on this scatterplot.
 
a. Does the scatterplot show there is a linear relationship between the average flow rate and pressure? (3 points)
. Does the scatterplot indicate a positive or negative linear relationship? (3 points)
c. Would the co
elation coefficient for this set of data be strong or weak? Why? (3 points
3. Answer the following questions about a co
elation coefficient of  0.102:
a. Does it indicate a weak or strong linear relationship between two variables? (3 points) Explain why. (3 points)
. Does it indicate a positive or negative linear relationship between two variables? (3 points) Explain why. (3 points)
4. What is the value of y' when x = 5, given the following equation of a regression line?
y' = XXXXXXXXXX8x
5. A vacation resort rents bicycles to tourists. The resort charges a deposit of $30 and a per hour fee of $8.50. If the total fee, F, is expressed in terms of the number of hours, x, that a bicycle is rented, the equation for the line that expresses that relationship between the variables is:
XXXXXXXXXXF = XXXXXXXXXX5x
a. What is the dependent variable? (3 points)
. What is the independent variable? (3 points)
c. What is the slope? (3 points)
d. What does the slope indicate about the relationship between the number of hours rented and the total fee? (3 points)
e. What would the total fee be if a bicycle is rented for 5 hours? (3 points)
6. The prices of stocks can fluctuate throughout any day. If the following linear equation represents the price of a stock and x is the number of hours passed in an eight-hour day of trading: y = 15 – 1.5x
What is the slope of the line and what does it mean? (4 points)
What is the y-intercept and what does it mean? (4 points)
If you owned this stock, would you want a positive or negative slope? Explain why. (4 points)
7. A psychologist wants to determine if there is a linear relationship between the number of hours a person goes without sleep and the number of mistakes he/she makes on a simple test. The following data is recorded.
                               
    Hours without Sleep, x 
    Number of Mistakes, y
    32
    6
    38
    8
    48
    13
    24
    5
    46
    7
    35
    6
    30
    5
    34
    8
    42
    12
    22
    3
a.  Draw a scatterplot of the data with paper and pencil. (4 points)
. Given r = 0.828 and the scatterplot you graphed in part (a), what is the relationship between the two variables? Include in your answer the strength and if it is positive or negative. (4 points)
c. If a = XXXXXXXXXXand b = 0.2997, write the regression equation for the variables. (3 points) (Note: y’ = a + bx)
d. Using the regression equation from part (c), determine the number of mistakes a person would make when getting 40 hours of sleep. (3 points)
8. Let S(t) be the retail sales in billions of dollars in t years since 1995. A linear model for the data is:
S(t) = 9.44t XXXXXXXXXX.
Use the model to predict the year in which retail sales will be $245 billion. Round to the nearest whole number.