can you also please explain me the meaning of r square, correlation, p value and

Question

can you also please explain me the meaning of r square, correlation, p value and stdev error value relating to my hypothesis. what these number signifies. how can i interpret it?

Year Population Total Accidents 2009 1566303 2044 2010 1515199 2545 2011 1524947 2560 2012 1539429 2690 2013 1561686 1961 2014 1610921 2110 Regression Analysis r2 0.518 r-0.720 Std. Error 244.088 Dep. Var. Total Accidents ANOVA table df 1 255,949.3515 4.30 459,578.9955 MS value 1069 Source F p- Regression 255,949.3515 Residual 238,315.9819 Total 494,265.3333 Regression out confidence interval variables cefficients std. error Intercept 12,455.8648 4,892.0614 0.0031 t(df-4) p-value 2.546 0636 2.0731069 95% upper -1,126.6752 26,038.4049 0.0022 95% lower Population -0.0065 0.0153 First table is the data and second is the Regression analysis and anova table from the excel. My hypothesis is that as the population increases, more accidents will occur annually. Can you please help me analysing the data and determine if my hypothesis is correct or not. And also help generate regression equation and interprete all outputs of the table. like what r square, r and std. error p value etc represents

Explanation / Answer

r square = it indicated how much proportion variation of dependent variable is explained by the regression model.

It is also called measure of goodness of fit.

here, r square = 0.518

it means that 51.8 of variation of y is explained by the regression model.

Correlation means the extend to linear association between variables.

That means the how much two variables are linearly related to each other.

here, correlation = -0.720

it means the variables have strong negative linear association.

if one increases other decreases.

p value:

The p-value is the level of marginal significance within a statistical hypothesis test . It represents the probability of occurence of the given event. if p value > level of significance, we fail to reject the null hypothesis.

here, overall p value = 0.1096

if it is > alpha then we say that the regession model is not significant.

if it is < alpha then the regression model is significant.

if p value < level if significance , we reject the null hypothesis.

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