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2 . To complete a painting job requires four hours setup time plus one hour per 1,000 square feet. How would you express this information in a linear equation?
3 . A statistics instructor is paid a per-class fee of $2,000 plus $100 for each student in the class. How would you express this information in a linear equation?
4 . A tutoring school requires students to pay a one-time enrollment fee of $500 plus tuition of $3,000 per year. Express this information in an equation.
Use the following information to answer the next four exercises. For the labor costs of doing repairs, an auto mechanic charges a flat fee of $75 per car, plus an hourly rate of $55.
5 . What are the independent and dependent variables for this situation?
6 . Write the equation and identify the slope and intercept.
7 . What is the labor charge for a job that takes 3.5 hours to complete?
8 . One job takes 2.4 hours to complete, while another takes 6.3 hours. What is the difference in labor costs for these two jobs?
9 . Describe the pattern in this scatter plot, and decide whether the X and Y variables would be good candidates for linear regression.
10 . Describe the pattern in this scatter plot, and decide whether the X and Y variables would be good candidates for linear regression.
11 . Describe the pattern in this scatter plot, and decide whether the X and Y variables would be good candidates for linear regression.
12 . Describe the pattern in this scatter plot, and decide whether the X and Y variables would be good candidates for linear regression.
Use the following information to answer the next four exercises. Height (in inches) and weight (In pounds) in a sample of college freshman men have a linear relationship with the following summary statistics:
$\overline{x}$ = 68.4
$\overline{y}$ =141.6
s
_{x} = 4.0
s
_{y} = 9.6
r = 0.73
Let
Y = weight and
X = height, and write the regression equation in the form:
$\widehat{y}=a+bx$
13 . What is the value of the slope?
14 . What is the value of the y intercept?
15 . Write the regression equation predicting weight from height in this data set, and calculate the predicted weight for someone 68 inches tall.
16 . The correlation between body weight and fuel efficiency (measured as miles per gallon) for a sample of 2,012 model cars is –0.56. Calculate the coefficient of determination for this data and explain what it means.
17 . The correlation between high school GPA and freshman college GPA for a sample of 200 university students is 0.32. How much variation in freshman college GPA is not explained by high school GPA?
18 . Rounded to two decimal places what correlation between two variables is necessary to have a coefficient of determination of at least 0.50?
19 . Write the null and alternative hypotheses for a study to determine if two variables are significantly correlated.
20 . In a sample of 30 cases, two variables have a correlation of 0.33. Do a
t -test to see if this result is significant at the
α = 0.05 level. Use the formula:
$t=\frac{r\sqrt{n-2}}{\sqrt{1-{r}^{2}}}$
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