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A researcher wants to determine if gas consumption is affected by the number of days below 65 degrees. The data are shown below for 9

A researcher wants to determine if gas consumption is affected by the number of days below 65 degrees. The data are shown below for 9 months:

Month

Average Number Days Below 65 Degrees

Gas Consumption

October

15.6

5.2

November

26.8

6.1

December

37.8

8.7

January

36.4

8.5

February

35.5

8.8

March

18.6

4.9

April

15.3

4.5

May

7.9

2.5

June

0

1.1

  1. Could you make a scatterplot of the data
  2. What is the correlation coefficient in terms of direction and strength.
  3. What is a hypothesis test to determine if there is a significant relationship between temperature and gas consumption. If there is a significant relationship, describe the relationship (e.g., as temperatures increase, the gas consumption...). Test using an alpha of .05.
  4. Could you run a regression equation to determine if there is a predictive relationship between temperatures and gas consumption.
    1. Which variable is the dependent variable (the one that is being predicted or the effect)?
    2. Which variable is the independent variable (the one that is being used to predict or the cause)?
  5. What is a statement about the cause and effect relationship that you will be estimating in the regression:
    1. I will be using _________________ to predict __________
  6. What Estimate the regression equation.
  7. Could you describe the intercept of the regression equation.
  8. Could you describe the slope of the regression equation.
  9. Could you run a hypothesis test to determine if there is a significant linear relationship between temperature and gas consumption. Test using an alpha of .05.
  10. What is the coefficient of determination? Describe that it means in terms of this regression equation.
  11. Use the regression equation to find the predicted values of the Temp (x) = 20.
  12. Use the regression equation to find the predicted values of the Temp (x) = 30.

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