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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.

12.2: slope and Y -intercept of a linear 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?

12.3: scatter plots

9 . Describe the pattern in this scatter plot, and decide whether the X and Y variables would be good candidates for linear regression.

This is a scatterplot. The points in the plot show a fairly strong, linear, uphill trend.

10 . Describe the pattern in this scatter plot, and decide whether the X and Y variables would be good candidates for linear regression.

This is a scatterplot. The points in the plot show a moderately strong, linear, downhill trend.

11 . Describe the pattern in this scatter plot, and decide whether the X and Y variables would be good candidates for linear regression.

This is a scatterplot. The points in the plot are spread across the graph and do not exhibit a strong trend of any kind.

12 . Describe the pattern in this scatter plot, and decide whether the X and Y variables would be good candidates for linear regression.

This is a scatterplot. The points in the plot show a strong, curved, upward trend.

12.4: the regression equation

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:
x ¯ = 68.4
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:
y ^ = a + b x

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.

12.5: correlation coefficient and coefficient of determination

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?

12.6: testing the significance of the correlation coefficient

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 = r n 2 1 r 2

Questions & Answers

limitations of simple random sampling
pratyaksh Reply
how can l calculate G. M from the following size 125 133 141 173 182 frequency 7 5 4 1 3
Stancy Reply
how they find mean population
Joy Reply
parts of statistics
Edwin Reply
what is a mean?
Onele Reply
given the sequence 128,64,32 find the 12th term of the sequence
Shehu Reply
12th number is 0.0625
Thangarajan
why do we use summation notation to represent set of observations
MICHAEL Reply
what is the potential outlier ?
Anik Reply
A pharmaceutical company claims that their pain reliever capsule is 70% effective. But a clinical test on this capsule showed 65 out of 100 effectiveness
jelly Reply
Part of statistics
charls Reply
how to find mean population
Dawit Reply
what is data value
Ravneet Reply
what is relative frequency
Adeyemi Reply
liner regression analysis
Swathy Reply
Proper definition of outlier?
Sumbal Reply

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Source:  OpenStax, Introductory statistics. OpenStax CNX. May 06, 2016 Download for free at http://legacy.cnx.org/content/col11562/1.18
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