AP Stats Final

30. Use Scenario 3-8. Which of the following is the plot of residuals versus fish lengths? A. B. C. D. E.

D.

48. Use Scenario 5-10. Find the value of and describe it in words. A. 0.1; The probability that the student takes both chemistry and Spanish. B. 0.1; The probability that the student takes either chemistry or Spanish, but not both. C. 0.5; The probability that the student takes either chemistry or Spanish, but not both. D. 0.6; The probability that the student takes either chemistry or Spanish, or both. E. 0.6; The probability that the student takes both chemistry and Spanish.

D. 0.6; The probability that the student takes either chemistry or Spanish, or both.

54. Use Scenario 6-15. A. 0.0518 B. 0.1296 C. 0.2592 D. 0.8704 E. 0.9482

D. 0.8704

49. Use Scenario 5-13. If a single student is selected at random, what is the probability associated with the union of the events "has a dog" and "does not have a cat?" A. 0.04 B. 0.16 C. 0.78 D. 0.9 E. 0.94

D. 0.9

P(at least one) =

1 - P (none)

What is percentile

The percent of values less than or equal to a given value

Sampling methods (voluntary response, convenience, SRS, stratified random sample, cluster sample, systematic sample)

Voluntary --> people choose Convenience --> easy to reach SRS --> label individuals, RNG, select individuals Stratified --> sample some from all groups Cluster --> sample all from only some groups Systematic --> choose random starting point and use equal intervals

Non-response

When an individual chooses to not respond, or they can't be reached

Statistically significant

When results are too unusual to have occurred purely by chance.

Undercoverage

When some members of the population cannot or are less likely to be in the sample

How to find the residual

actual - prediction

42. Event A has probability 0.4. Event B has probability 0.5. If A and B are disjoint, then the probability that both events occur is A. 0.0. B. 0.1. C. 0.2. D. 0.7. E. 0.9.

A. 0.0.

For any distribution, what effect does adding/subtracting "a" and multiplying/dividing "b"

"a" --> shape/variability stay the same, center +/- "a" "b" --> shape stays same, center/variability */÷ by "b"

1 - binomcdf/1 - geometcdf

"at least" "_____ or more" P ≥ ____)

Binomcdf/geometcdf

"at most" "______ or fewer" P(x ≤ ___)

Binompdf/geometpdf

"exactly ______ correct" P(x = _____)

invNorm

(area, mean, SD) --> when there is a probability

how to use normalcdf

(lower, upper, mean, SD) --> when there's not a probability

probability of continuous random variable (uniform or normal) to get the probability of an event

* find area under the curve * Uniform --> 1/k Normal --> N(mean, SD) z= # - mean / SD Table A OR normalcdf

68-95-99.7 rule

68% of the population is within 1 standard deviation of the mean (34% and 34%). 95% of the population is within 2 standard deviation of the mean (13.5% and 13.5%). 99.7% of the population is within 3 standard deviation of the mean (2.35% and 2.35%).

18. Birthweights at a local hospital have a Normal distribution with a mean of 110 oz. and a standard deviation of 15 oz. The proportion of infants with birthweights under 95 oz. is about A. 0.159. B. 0.025. C. 0.341. D. 0.500. E. 0.841.

A. 0.159.

52. Use Scenario 6-12. Which of the following expresses the probability that the student gets no questions correct? A. B. C. D. E.

B.

53. Use Scenario 6-14. If you randomly select 20 bottles from those produced by this machine, what is the approximate probability that between 2 and 6 (inclusive) caps have been improperly applied? A. 0.19 B. 0.26 C. 0.38 D. 0.74 E. 0.92

B. 0.26

57. Use Scenario 6-5. The standard deviation of the number of customers that make a purchase during the first hour that the store is open is A. 0.2. B. 1.4. C. 2.0. D. 3.0. E. 4.0.

B. 1.4.

Binomial vs geometric

Binomial --> Binary, Independent, Number of trials, Probability of success (BINS), when there is a fixed amount of trails (mean = n-p (SD = √np (1-p) Geometric --> Binary, Independent, Trials until success, same probability (BITS), trials until first success, ALWAYS skewed right (mean = 1/p) (variability = √1-p / p)

22. Use Scenario 3-1. If the data point (65,70) were removed from this study, how would the value of the correlation r change? A. r would be smaller, since there are fewer data points. B. r would be smaller, because this point falls in the pattern of the rest of the data. C. r would be larger, since the x and y coordinates are larger than the mean x and mean y, respectively. D. r would be larger, since this point does not fall in the pattern of the rest of the data. E. r would not change, since it's value does not depend which variable is used for x and which is used for y.

D. r would be larger, since this point does not fall in the pattern of the rest of the data.

Describing relationship between scatterplot

Direction (+,-, none), Unusual features, Form (linear, non-linear), Strength (strong, moderate, weak) (DUFS) +context

4. Use Scenario 1-1. Which of the following graphs accurately represents the distribution for political party registration for each gender? A. B. C. D. E.

E.

Frequency, relative frequency, cumulative relative frequency

Frequency --> counts Relative frequency --> % Cumulative Relative Frequency --> percentile

How do outliers and influential points on the LSRL affect line?

Horizontal outliers --> tilt the line (see-saw) Vertical outliers --> shifts line up or down

Law of large numbers

If we do something many many times the proportion of desired outcomes will approach its probability

What is affected by outliers?

Mean and SD

5 number summary?

Minimum, Q1 (median of 1st quartile), Median, Q3 (median of 2nd quartile), Maximum

Sampling errrors

Mistakes made in the process of sampling like choosing a bad method (voluntary response or undercoverage)

Observational vs experimental study

Observational --> no treatment Experimental --> treatments imposed, shows causation

Non-sampling errors

Problem after sample was chosen like response bias, non-response bias, or wording of the question

Purpose of random assignment/sampling

Random sample --> to generalize our conclusions to the population from what we sampled Random assignment --> to say a treatment causes changes in the response variable

How to find the SD from the variance

SD^2 = variance

How to describe a distribution

Shape, Outliers, Center, Variability (SOCV) +context and compare

Mean vs median when graph is skewed right, left, or symmetric

Skewed right --> median less than mean Skewed left --> median greater than mean Symmetric --> median and mean equal

Probability rules (complement rule, general addition rule, general multiplication rule)

complement --> probability of an event not happening P(A complement) = 1 - P(A) general addition "OR" --> P(A or B) = P(A) + P(B) general multiplication "AND" --> P(A and B) = P(A) * P(BIA)

Experimental designs (completely randomized design, randomized block design, matched pairs design)

completely randomized --> one where the treatments are assigned completely at random so that each experimental unit has the same chance of receiving any one treatment randomized block --> separate subjects into blocks and then randomly assign treatments within each block matched pairs --> subjects who are paired and randomly assigned a treatment (each subject receives two treatments in random order)

Interpret correlation, slope, y-intercept, residual, r^2, and SD of residuals

correlation --> direction, always linear form, strength slope --> "with each additional (x-context) the predicted (y-context) (increases/decreases) by (slope)." y-intercept --> "when x=0 (context) the predicted (y-context) is (y-int)." residual --> "the actual (context) was (residual) (above/below) the predicted value for (x= #)." r^2 --> "About (r^2) % of the variability in (y-context) is accounted for by the LSRL." SD --> "The actual (y-context) is typically about (s) away from the number predicted by the LSRL."

Least squares regression line equation?

expected value = y-intercept + slope (ŷ = a + bx)

z score formula/interpretation

formula --> (value - mean) / (SD) interpretation --> "(context) is (z) standard deviations (above/below) the mean"

Discrete random variables: find mean and SD

mean = Xi(Pi) 1(0.15/1)+2(.42/1)+3(.32/1)....... SD: σ = √Σ(xi-μ)2 * P(xi)

Binomial distribution: find mean and SD

mean = np SD = √np(1-p)

Geometric distribution: find mean and SD

mean = np SD = √np(1-p)

If the distribution is symmetric, what should you use to describe it?

mean or SD

If the distribution has outliers or it is skewed, what should you use to describe it?

median or IQR

Random sample w/o replacement is independent if....

n (sample size) ≤ .10 N (population)

Normal approximation if...

np ≥ 10 AND n(1-p) ≥ 10

Response bias

pattern of inaccurate responses (wording, interviewer, lying)

IQR rule?

way to small if low outlier < Q1 - 1.5(IQR) way too big if high outlier > Q3 + 1.5(IQR)

29. Use Scenario 3-8. The equation of the least-squares regression line is A. Eggs = -142.74 + 39.25(Length) B. Eggs = 39.25 - 142.74(Length) C. Eggs = 25.55 + 5.392(Length) D. Eggs = 25.55 + 5.392(Eggs) E. Eggs = -142.74 + 39.25(Eggs)

A. Eggs = -142.74 + 39.25(Length)

3. In a study of the link between high blood pressure and cardiovascular disease, a group of white males aged 35 to 64 was followed for 5 years. At the beginning of the study, each man had his blood pressure measured and it was classified as either "low" systolic blood pressure (less than 140 mm Hg) or "high" blood pressure (140 mm Hg or higher). The following table gives the number of men in each blood pressure category and the number of deaths from cardiovascular disease during the 5-year period. Based on these data, which of the following statements is correct? A. These data are consistent with the idea that there is a link between high blood pressure and death from cardiovascular disease. B. The mortality rate (proportion of deaths) for men with high blood pressure is 5 times that of men with low blood pressure. C. These data probably understate the link between high blood pressure and death from cardiovascular disease, because men will tend to understate their true blood pressure. D. Although there were more deaths in the high blood pressure group, this is expected, because there were 1500 more men in that group. E. All of the above.

A. These data are consistent with the idea that there is a link between high blood pressure

31. A television station is interested in predicting whether voters in its viewing area are in favor of offshore drilling. It asks its viewers to phone in and indicate whether they support/are in favor of or are opposed to this practice. Of the 2241 viewers who phoned in, 1574 (70%) were opposed to offshore drilling. The viewers who phoned in are A. a voluntary response sample. B. a convenience sample. C. a probability sample. D. a population. E. a simple random sample.

A. a voluntary response sample.

46. Use Scenario 5-3. The events A = the next two babies are boys, and B = the next two babies are girls are A. disjoint. B. conditional. C. independent. D. complementary. E. none of the above.

A. disjoint.

36. Use Scenario 4-5. This is a(n) A. observational study. B. experiment, but not a double blind experiment. C. double blind experiment. D. matched pairs experiment. E. block design.

A. observational study.

38. A study of elementary school children, ages 6 to 11, finds a high positive correlation between shoe size x and score y on a test of reading comprehension. The observed correlation is most likely due to A. the effect of a lurking variable, such as age. B. a mistake, since the correlation must be negative. C. cause and effect (larger shoe size causes higher reading comprehension). D. "reverse" cause and effect (higher reading comprehension causes larger shoe size. E. several outliers in the data set.

A. the effect of a lurking variable, such as age.

Describe the effect on the mean and standard deviation of a random variable when you add/subtract or multiply/divide by a constant, or combine random variables

Adding/subtracting --> shape (same), center (add/subtract), variability (same) Multiplying/dividing --> shape (same), center (multiply/divide), variability (multiply/divide)

26. Use Scenario 3-7. The circled point on the scatter plot represents lima beans, which have 621 calories and 37 grams of protein. The residual for lima beans is: A. -37.0 B. -4.18 C. 4.18 D. 37.0 E. 41.18

B. -4.18

59. Use Scenario 6-17. You're going to give up and call a tow truck if you don't find jumper cables by the time you've asked 10 people. What's the probability you end up calling a tow truck? A. 0.8251 B. 0.1749 C. 0.1344 D. 0.0333 E. 0.0280

B. 0.1749

11. A lobster fisherman is keeping track of the productivity of a set of traps he has placed in a favorite location. Below are the numbers of lobsters in these traps over the course of 12 different hauls. 0 3 3 3 4 5 5 6 7 7 12 14 According to the 1.5 x IQR rule, which values in the above distribution are outliers? A. 0 only B. 14 only C. 12 and 14 D. 0 and 14 E. 0, 12, and 14

B. 14 only

19. The time to complete a standardized exam is approximately Normal with a mean of 70 minutes and a standard deviation of 10 minutes. How much time should be given to complete the exam so that 80% of the students will complete the exam in the time given? A. 61.6 minutes B. 78.4 minutes C. 79.8 minutes D. 84 minutes E. 92.8 minutes

B. 78.4 minutes

10. Use Scenario 1-4. Which of the following is a correct box plot for these data? A. A B. B C. C D. D E. E

B. B

1. A professor records the values of several variables for each student in her class. These include the variables listed below. Which of these variables is categorical? A. Score on the final exam (out of 200 points). B. Final grade for the course (A, B, C, D, or F). C. The total number of points earned in the class (i.e., the total of the points on all exams and quizzes in the course; the maximum number of points possible is 500). D. The number of lectures the student missed. E. Amount of time, in minutes, spent studying for the final exam.

B. Final grade for the course (A, B, C, D, or F).

27. Students with above-average scores on Exam 1 in STAT 001 tend to also get above-average scores on Exam 2. But the relationship is only moderately strong. In fact, a linear relationship between Exam 2 scores and Exam 1 scores explains only 36% of the variance of the Exam 2 scores. A. The correlation between Exam 1 scores and Exam 2 scores is r = .36. B. The correlation between Exam 1 scores and Exam 2 scores is r = .6. C. The correlation between Exam 1 scores and Exam 2 scores is r = ± .36 (can't tell which). D. The correlation between Exam 1 scores and Exam 2 scores is r = ± .6 (can't tell which). E. There is not enough information to say what r is.

B. The correlation between Exam 1 scores and Exam 2 scores is r = .6.

12. For the density curve below, which of the following is true? A. The median is 0.5. B. The median is larger than 0.5. C. The density curve is skewed right. D. The density curve is Normal. E. The density curve is symmetric.

B. The median is larger than 0.5.

35. A local tax reform group polls the residents of the school district and asks the question, "Do you think the school board should stop spending taxpayers' money on non-essential arts programs in elementary schools?" The results of this poll are likely to A. Underestimate support for arts programs because of undercoverage. B. Underestimate support for arts programs because of nonsampling error. C. Overestimate support for arts programs because of undercoverage. D. Overestimate support for arts programs because of nonsampling error. E. Accurately estimate support for arts programs.

B. Underestimate support for arts programs because of nonsampling error.

13. You are told that your score on an exam is at the 85 percentile of the distribution of scores. This means that A. Your score was lower than approximately 85% of the people who took this exam. B. Your score was higher than approximately 85% of the people who took this exam. C. You answered 85% of the questions correctly. D. If you took this test (or one like it) again, you would score as well as you did this time 85% of the time. E. 85% of the people who took this test earned the same score you did.

B. Your score was higher than approximately 85% of the people who took this exam.

16. Use Scenario 2-1. The mean salary for the employees will A. be unchanged. B. increase by $3,000. C. be multiplied by $3,000. D. increase by $3,000 E. increase by $150.

B. increase by $3,000.

21. Two variables are said to be negatively associated if A. larger values of one variable are associated with larger values of the other. B. larger values of one variable are associated with smaller values of the other. C. smaller values of one variable are associated with smaller values of the other. D. smaller values of one variable are associated with both larger or smaller values of the other. E. there is no pattern in the relationship between the two variables.

B. larger values of one variable are associated with smaller values of the other.

58. Use Scenario 6-10. Here's Albert's game: You give him $10 each time you roll, and he pays you (in dollars) the amount that comes up on the dice. If P = the amount of money you gain each time you roll, the mean and standard deviation of P are: A. B. C. D. E.

C.

43. Event A has probability 0.4. Event B has probability 0.5. If A and B are independent, then the probability that both events occur is A. 0.0. B. 0.1. C. 0.2. D. 0.7. E. 0.9.

C. 0.2.

2. You measure the age (years), weight (pounds), and marital status (single, married, divorced, or widowed). of 1400 women. How many variables did you measure? A. 1 B. 2 C. 3 D. 1400 E. 1403

C. 3

20. Entomologist Heinz Kaefer has a colony of bongo spiders in his lab. There are 1000 adult spiders in the colony, and their weights are Normally distributed with mean 11 grams and standard deviation 2 grams. About how many spiders are there in the colony which weigh more than 12 grams? A. 117 B. 160 C. 310 D. 690 E. 840

C. 310

25. Use Scenario 3-6. The y-intercept of the least-squares line is A. -10.95 B. 4.52 C. 4.65 D. 8.48 E. 8.55

C. 4.65

17. The Normal curve below describes the death rates per 100,000 people in developed countries in the 1990's. The mean and standard deviation of this distribution are approximately A. Mean 100; Standard Deviation 65 B. Mean 100; Standard Deviation 100 C. Mean 190; Standard Deviation 65 D. Mean 190; Standard Deviation 100 E. Mean 200; Standard Deviation 130

C. Mean 190; Standard Deviation 65

51. For which of the following counts would a binomial probability model be reasonable? A. The number of traffic tickets written by each police officer in a large city during one month. B. The number of hearts in a hand of five cards dealt from a standard deck of 52 cards that has been thoroughly shuffled. C. The number of 7's in a randomly selected set of five random digits from a table of random digits. D. The number of phone calls received in a one-hour period. E. All of the above.

C. The number of 7's in a randomly selected set of five random digits from a table of random digits.

5. Use Scenario 1-2. Which of the following is a marginal distribution? A. The percentage of all four-cylinder cars manufactured in Germany. B. The number of four-cylinder cars manufactured in Germany. C. The percentage of all cars manufactured in each country. D. The percentage of cars manufactured in Germany for each number of cylinders. E. The numbers 4, 5, 6, 8.

C. The percentage of all cars manufactured in each country.

34. A stratified random sample is appropriate when A. It is impractical to take a simple random sample because the population is too large. B. The population can be easily subdivided into groups according to some categorical variable, and the variable you are measuring is quite different within the groups but very similar between groups. C. The population can be easily subdivided into groups according to some categorical variable, and the variable you are measuring is very similar within the groups but quite different between groups. D. You intend to take a sample of more than 100 individuals. E. You want to avoid undercoverage of certain groups.

C. The population can be easily subdivided into groups according to some categorical

6. One way economists measure the health of the real estate market is by counting "housing starts," or the number of permits issued for construction of new homes. Below is a graph displaying housing starts (in thousands) in the United States from 2006 to 2009. What is the principle weakness of this graphical presentation of data? A. The "thousands" label on the vertical scale is confusing and misleading. B. The data only shows housing starts for four years, which is not enough time to identify a meaningful trend. C. Using proportionally-sized pictograms exaggerates the difference between years. D. Data of this type should only be displayed in a pie chart. E. It is unclear which dimension of the house represents the number of housing starts for that year.

C. Using proportionally-sized pictograms exaggerates the difference between years.

39. A double-blind experiment was conducted to evaluate the effectiveness of the Salk polio vaccine. The purpose of keeping the diagnosing physicians ignorant of the treatment status of the experimental subjects was to A. eliminate grounds for malpractice suits. B. ensure that subjects were randomly assigned to treatments. C. eliminate a possible source of bias. D. make sure nobody is harmed. E. prevent stratification of the experiment.

C. eliminate a possible source of bias.

37. Use Scenario 4-7. The brand of pellets is A. a parameter. B. the response variable. C. the explanatory variable. D. the placebo effect. E. a lurking variable.

C. the explanatory variable.

56. Use Scenario 6-1. The probability of at least one tail is A. 0.2500. B. 0.3125. C. 0.6875. D. 0.9375. E. none of these.

D. 0.9375.

24. Use Scenario 3-4. Based on the scatterplot, the least-squares line would predict that a car that emits 10 grams of CO per mile driven would emit approximately how many grams of NOX per mile driven? A. 10.0 B. 1.7 C. 2.2 D. 1.1 E. 0.7

D. 1.1

60. Use Scenario 6-6. The probability that X is between 0.5 and 1.5 is A. 3/4. B. 1. C. 1/4. D. 1/2. E. 1/3.

D. 1/2.

The following histogram represents the distribution of acceptance rates (percent accepted) among 25 business schools in 1997. What percent of the schools have an acceptance rate of under 20%? A. 3% B. 4% C. 12% D. 16% E. 24%

D. 16%

32. Use Scenario 4-1. The newspaper asks you to comment on their survey of local opinion. You say: A. This is a simple random sample. It gives very accurate results. B. This is a simple random sample. The results are not biased, but the sample is too small to have high precision. C. This is a census, because all fans had a chance to be asked. It gives very accurate results. D. This is a convenience sample. It will almost certainly overestimate the level of support among all Lafayette residents. E. This is a convenience sample. It will almost certainly underestimate the level of support among all Lafayette residents.

D. This is a convenience sample. It will almost certainly overestimate the level of support

47. Event A occurs with probability 0.3, and event B occurs with probability 0.4. If A and B are independent, we may conclude that A. P(A and B) = 0.12. B. P(A|B) = 0.3. C. P(B|A) = 0.4. D. all of the above. E. none of the above.

D. all of the above.

40. An experiment compares the taste of a new spaghetti sauce with the taste of a commercially successful sauce readily available in grocery stores. Each of a number of tasters tastes both sauces (in random order) and says which tastes better. This is called a A. simple random sample. B. stratified random sample. C. completely randomized design. D. matched pairs design. E. double-blind design.

D. matched pairs design.

55. A college basketball player makes 5/6 of his free throws. Assuming free throw attempts are independent, the probability that he makes exactly three of his next four free throws is A. B. C. D. E.

E.

44. Use Scenario 5-3. The probability that the next five babies are girls is A. 1.0. B. 0.5. C. 0.1. D. 0.0625. E. 0.03125.

E. 0.03125.

50. Use Scenario 5-7. If a randomly selected person is tested and the result is positive, the probability the individual has the disease is A. 0.001. B. 0.019. C. 0.020. D. 0.021. E. 0.047.

E. 0.047.

45. Use Scenario 5-3. The probability that at least one of the next three babies is a boy is A. 0.125. B. 0.333. C. 0.667. D. 0.750. E. 0.875.

E. 0.875.

41. A basketball player makes 75% of his free throws. We want to estimate the probability that he makes 4 or more frees throws out of 5 attempts (we assume the shots are independent). To do this, we use the digits 1, 2, and 3 to correspond to making the free throw and the digit 4 to correspond to missing the free throw. If the table of random digits begins with the digits below, how many free throw does he hit in our first simulation of five shots? 19223 95034 58301 A. 1 B. 2 C. 3 D. 4 E. 5

E. 5

14. The five-number summary of the distribution of 316 scores on a statistics exam is: 0 26 31 36 50 The scores are approximately Normal. The standard deviation of test scores must be about A. 0.67. B. 5.0. C. 10. D. 55. E. 7.5.

E. 7.5.

28. Which of the following statements describes what the standard deviation of residuals for a regression equation can be used for? I. It describes the typical vertical distance between an observed data point and the regression line. II. It evaluate whether a linear model is appropriate for a set of data. III. It measures the overall precision of predictions made using the regression equation. A. I only B. II only C. III only D. Both I and II E. Both I and III

E. Both I and III

8. The median age of five elephants at a certain zoo is 30 years. One of the elephants, whose age is 50 years, is transferred to a different zoo. The median age of the remaining four elephants is A. 40 years. B. 30 years. C. 25 years. D. less than 30 years. E. Cannot be determined from the information given.

E. Cannot be determined from the information given.

9. You want to use numerical summaries to describe a distribution that is strongly skewed to the left. Which combination of measure of center and spread would be the best ones to use? A. Mean and interquartile range. B. Mean and standard deviation. C. Median and range. D. Median and standard deviation. E. Median and interquartile range.

E. Median and interquartile range.

15. An ecologist studying starfish populations collected starfish of the species Pisaster was interested in the distribution of sizes of starfish on a certain shoreline. One measure of size is "arm length." Below is a cumulative frequency distribution for the arm length of 102 Pisaster individuals. The median and interquartile range of this distribution are approximately: A. Median is 15.2; Intequartile range is 12.5 to 16.8 B. Median is 13; Interquartile range is 13 to 16.1 C. Median is 13; Interquartile range is 3.1 D. Median is 13; Intequartile range is 4.3 E. Median is 15.2; Intequartile range is 4.3

E. Median is 15.2; Intequartile range is 4.3

33. An example of a nonsampling error that can reduce the accuracy of a sample survey is A. using voluntary response to choose the sample. B. using the telephone directory as the sampling frame. C. interviewing people at shopping malls to obtain a sample. D. variation due to chance in choosing a sample at random. E. many members of the sample cannot be contacted.

E. many members of the sample cannot be contacted.

23. The correlation coefficient measures A. whether there is a relationship between two variables. B. the strength of the relationship between two quantitative variables. C. whether or not a scatterplot shows an interesting pattern. D. whether a cause and effect relation exists between two variables. E. the strength of the linear relationship between two quantitative variables.

E. the strength of the linear relationship between two quantitative variables.

Least squares regression line slope/y-intercept formulas?

Slope: b = r(Sy/Sx) Y-intercept: a = ȳ - bx̄