a) the correlation coefficient is calculate using correlation function in Excel
"CORREL (array1, array2) = 0.977"
The following needs to be tested:
"Null: \\rho = 0"
"Alternative:\\rho\\ne0"
The sample size = 10. This means DF = n-2 =10 -2 =8
The corresponding critical correlation value "r_c" for a significance level of "\\alpha =0.05", for a two-tailed test is:
"r_c =0.632"
Observe that in this case, the null hypothesis "H_0: \\rho = 0" is rejected if "|r| >r_c =0.632"
we have that "|r| =0.977 > r_c=0.632" , from which is concluded that the null hypothesis is rejected. There is a significant correlation.
b) Regression from Excel toolPak has following output predicting prices
The regression model equation: "Price (Ksh) =2.424 length (pages) + 259.729"
c) Testing the model
"R^2" indicates there is goodness-of-fit because 95.44% of the variation on prices is contributed by the model. Overall, the model is statistically is significant since "F(1,8) =167.08, p-value < 0.05" . The regression coefficient for length is also statistically significant because the corresponding t-stat has a "p-value < 0.05."
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