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Mar 31st, 2015
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  1. Variable Coeff s.e. of Coeff T P
  2. constant 7288.54 6591 1.11 0.2826
  3. car age 11630.6 1249 9.31 0.0001
  4. S= 19280, 19 df R^2 = 0.82 R^2 (adj) = 0.811
  5.  
  6. ok so
  7. this is a run through of how to read the output
  8. (this uses the line formula as y = a + bx)
  9.  
  10. you can safely ignore the whole first row besides the constant coefficient
  11. you can also ignore R^2 (adj). this value means nothing in the scope of AP stats
  12.  
  13. a = constant coefficient
  14. b = car age coefficient
  15.  
  16. the R^2 value for your line is 0.82
  17.  
  18. the standard deviation of your slope is the "s.e. of coefficient" value: 1249
  19. ^^also know how to do this formulaically though, one frq just gives you a table of values where you have to do everything from, but the other gives you a minitab output and no data, so you have to be able to know how to get SE *both* from minitab *and* by hand.
  20.  
  21. the t statistic of the slope your data said (that 11630.6 val) is 9.31. this is 11630.6 - 0 over 1249. they do that simple math for you since they love you.
  22.  
  23. the p value is the result if you do tcdf(9.31, 100000, 19), which is 0.0001. they do that for you too.
  24.  
  25. the S value is your standard error from the line. this is the sum of squared residuals over n-2 all in a root.
  26.  
  27. PART A:
  28. the formula of your line is
  29. yhat = 7288.54 + 11630.6*x
  30. yhat = predicted mileage of car
  31. x = age of the car
  32.  
  33. PART B:
  34. plug in 6 years in as x.
  35. the yhat value you get.
  36. use her value (65k) - yourpredictedyhatvalue to get her residual = -12072. this means that the line overestimated her mileage by about 12k.
  37.  
  38. PART C:
  39. for every year a car ages, it is driven 11630.6 miles.
  40.  
  41. PART D:
  42. correlation = r
  43. they give you r^2 is .82
  44. r = 0.9055385138....
  45. you know this is +0.905 instead of -0.905 because the slope of your line is positive (so mileage goes *up* as age goes up... which also makes logical sense, cars can't *lose* mileage)
  46. interpreting this value: there is a strong positive linear relationship between the age of a car and how many miles it has been driven. [general form: there is a strong ___ linear relationship between (explanatory variable) and (response variable).]
  47.  
  48. PART E:
  49. The line fits the data sort of well.
  50. S is 19280. this is pretty big. this means that on average, your line differed from the actual values by about 19k miles. so not terribly accurate... but the scatterplot of the residuals shows mostly equal variation, so our line is pretty nice. there were a few strong outliers where the actual value was far above the predicted value, and this kind of skewed our line to overpredict values for the most part, since the majority of the residual points are under the line y = 0... but overall, the line is pretty good.
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