DC Households. Use the following information for Exercises 59–61. The data set Households, located on the text Web site, contains information on the number and type of households in the 50 states and the District of Columbia. For each state, there are seven variables. Two of these variables are the percentage of households headed by women and the total number of households in the state . Minitab provides the following regression equation:

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Note: Minitab shows its regression equations as instead of . Also, the notation 2.82E-07 refers to the scientific notation method of writing numbers. Often, software and calculators will present you with this type of notation, so you need to know how to read it. The number 2.82E-07 represents 2.82 times , or 0.000000282.

Question 4.157

households

59. In this exercise, we explore the regression coefficients and the regression equation.

  1. Find and interpret the meaning of the value for the intercept. Does it make sense?
  2. Would the estimate in (a) be considered extrapolation? Why or why not?
  3. Find and interpret the meaning of the slope coefficient as the total number of households in the state increases.
  4. Write the regression equation. Now state in words what the regression equation means.
  5. Is the correlation coefficient positive or negative? How do you know?

4.2.59

(a) 10.5. In a state with 0 households, 10.5% of the households are headed by women. Since all states have households, the value would not occur. (b) This estimate would be considered extrapolation since the value of is outside the range of -values in the data set. (c) 0.000000282. For each increase of one household, the percentage of households headed by women increases by 0.000000282. (d) (Percentage of households headed by women) = 10.5 + 0.000000282 (Total number of households). The estimated percentage of households headed by women equals 10.5 plus 0.000000282 times the total number of households. (e) Positive since the slope is positive.