Question

DETROIT (Y) ANN ARBOR (X)

2008       59                           2008       61

2009       60                           2009       58

2010       61                           2010       60

2011       69                           2011       68

2012       66                           2012       67

2013       62                           2013       64

2014       64                           2014       66

2015       71                           2015       70

2016       69                           2016       72

2017       66                           2017       64

h₀  :There is a statistical correlation between the temperatures in two different Michigan cities.

Please show all five steps of hypothesis testing for regression and correlation analysis. Make sure you show all five steps with the appropriate format for the regression test you are using. Make sure you are consistent with your x and y variables. You indicated in the introduction section which data set is y (dependent) and which is x (independent). Be consistent here. Also remember that you run regression analysis on raw data, not sorted data.

Step 1

Step 2

Step 3

Correlation Coefficient
Coefficient of Determination
Standard Error
P-value
Regression Equation

Step 4

Step 5

What relationships exist between the data sets? Are they significant and why?

Answer 1

1)

define hypothesis:

h0:there is no correlation between x and y

ha: there is correlation between x and y

2)

set signifiance level: a

3)

calculate statistic: using Excel solver

Correlation Coefficient	.906
Coefficient of Determination	.0822
Standard Error	1.86
P-value	.0002
Regression Equation

step 4

create rejection/acceptence region

as p val<.05 we reject the null

step 5 conclusion

we can say that there is signifianct correlation between x and y