Data Science Classroom Series – 09/Nov/2021

Estimators and Estimates

  • An Estimator is a mathematical function approximates a population parameter depending on sample information.
  • Estimators have two important properties
    • Bias:
      • The expected value of an unbiased estimator is the population parameter. The bias in this case is zero
      • If the expected value of an estimator is (parameter+b), then the bias is b.
    • Efficiency:
      • The most effecient estimator is the one with smallest variance
  • Estimates:
    • An estimate is the output that you get from estimator (when you apply some formula).
    • There are two types of estimates
      • Point Estimate:
        • A single value
        • Examples:
          • 1
          • 5
          • 10000
          • 122.47
          • 0.32
      • Confidence Interval:
        • An interval
        • Example:
          • (0,3)
          • (4,8)
          • (9050, 10050)
          • (-0.70, 0.56)
        • A confidence interval is an interval within whic we are confident (with a certain percentage of confidence) the population parameter will fall.
        • Example: You have visited to 5% of the restaurants in hyderbad and found from the sample the average price of biryani is 225 Rs. So now you are 95% confident that the average biryani price in hyderabad will be in the range of (180, 275)
        • (1-α) is the level of confidence
          • If we want 90% confidence α = 10% => 0.1
          • If we want 95% confidence α = 5% => 0.05
          • If we want 99% confidence α = 1% => 0.01 Calculating Confidence Interval

  • While calculating confidence intervals we have two different situations

    • Known Population Variance
    • Unknown Population Variance
  • Lets Go with Known Population Variance:

    • General formula Preview
  • Consider the following xls which z-values Refer Here

  • Lets consider the following data set which has data scientist salaries sample. Since we are using Estimations with known variance. Std dev of the population $15000. Refer Here

  • Lets calculate the sample mean and standard error Preview

  • Lets calculate the Confidence intervals with 99% confidence and then 95% confidence

    • α = 1% => 0.01
    • α/2 => 0.005 Preview
  • Calculate Confidence intervals with 90% confidence Preview

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