530 144 10120 7 2754 EFGHG 53 HII HG 144 and 10We had these values from the

530 144 10120 7 2754 efghg 53 hii hg 144 and 10we had

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∑ ࠵? = 530 ; ∑ ࠵? = 144 ; ∑ ࠵?࠵? = 10120 ; ∑ ࠵? 7 = 2754 ; ࠵? : = EFG HG = 53 ; ࠵? : = HII HG = 14.4 and ࠵? = 10 We had these values from the table in our previous discussion. ࠵? = HG(HGH7G)Z(HII)(EFG) HG(7^EI)Z(HII) [ = 3.66 ࠵? = 53 − (3.66)(14.4) = 0.3 From our ࠵? 7 formula; ࠵? 7 = W ∑ ;XY ∑ =;Z<; : [ ∑ ; [ Z<; : [ ࠵? 7 = (G.F)EFGXF.__(HGH7G)ZHG(EF) [ F^‘EGZHG(EF) [ = 0.933
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This means that about 93% of the variations in fire damages to property is explained by variations in distance from the fire station. There is also a relationship between the Pearson Product Moment correlation coefficient (r) and the coefficient of determination. When you square the Pearson product moment coefficient you get the coefficient of determination (R 2 ). In other words, when you take a square root of the coefficient of determination ( ࠵? 7 ) and use the sign of the coefficient (b), you get the Pearson Product Moment correlation coefficient (r). Below are the some elements of r r ranges from -1.0 to 1.0 that is −1 ≤ ࠵? ≤ 1 The larger the absolute value of r ( |࠵?| ) is, the stronger is the relationship r near zero indicates there is no linear relationship between X and Y, and the scatter diagram appears to have no clear trend. If there is no relationship then ࠵? = 0 ࠵? = −1 or ࠵? = 1 implies that a perfect relationship between the two variables, that is, a single line will go through each point in a scatter diagram. We can say that X and Y are perfectly correlated Values of ࠵? = 0 , ࠵? = −1 and ࠵? = 1 are rare in practice The sign of r tells you whether the relationship between X and Y is positive (direct or moves in the same direction) or negative (inverse or moves in the opposite direction). The value of r tells very little about the slope of the line through the points on the scatter diagram (except the sign). If r is positive, the line through those points has a positive slope, and similarly, the line will have a negative slope if r is
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negative. A high r (e.g. r = 0.9) does not mean the slope is steep, since a flat line can also have a high r as r = 0.9. Testing for the significance of the correlation coefficient We test for the significance of the correlation coefficient (r) by using hypothesis testing. Note: Research is very expensive so in performing a research, we select a sample from a population. Therefore, after getting the results of the research, we have to find out if the sample results are a good representation of the population. We therefore follow some procedure to test whether the sample results are the same as the population. population Sample A hypothesis is a claim (assertion) about a population parameter We follow this five steps procedure. Steps: 1. State the hypothesis. Null Hypothesis ( ࠵? G ): We begin with the assumption that the Null hypothesis is true. (This is similar to the notion of innocent until proven guilty). Refers to the status quo or historical value
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Always contains “=“, or “ ”, or “ ” sign May or may not be rejected Alternative Hypothesis ( ࠵? H ): Is the opposite of the null hypothesis Challenges the status quo Never contains the “=“, or “ ”, or “ ” sign May or may not be proven
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