A breeder of golden retriever dogs has kept records on litter size for several years. They want to know if litter size is dependent on parent age. Age of Sire 9.0 7.0 6.5 4.3 5.0 4.1 3.7 8.0 7.0 4.1 4.5 7.0 6.0 Age of Dam 2.0 2.5 4.0 3.3 6.0 5.0 4.5 4.1 8.2 2.4 2.9 3.7 4.0 Litter Size 11 10 9 12 5 9 9 8 7 10 12 10 9 b. Perform a regression analysis. Define your hypothesis, state your conclusions, and show all work.

The records of litter size for several years of golden retrievers are given below:Age of sireAge of damLitter size921172.5106.5494.33.3125654.1593.74.5984.1878.274.12.4104.52.91273.710649The relevant hypotheses are: There is no linear relationship between parent age and litter size. There is a linear relationship between parent age and litter size.The general form of regression equation is , where, is the intercept, are the slope coefficients of 'age of sire' and 'age of dam' respectively and , are the independent variables 'age of sire' and 'age of dam'.Multiple regression can be performed using Excel.Steps to follow are given below:Enter the data in Excel.Highlight the data.Go to Data > Data analysis.Select Regression, click ok.Enter Y range i.e., litter size.Enter X range i.e., age of sire and age of dam.Set alpha level as 0.05.Select the output range.Click,ok.Enter Y range i.e., litter size.Enter X range i.e., age of sire and age of dam.Set alpha level as 0.05.Select the output range.Click ok.Excel output is shown below:Using the coefficients, the equation of the multiple regression model is:.From the output, the F-statistic is 7.414 and the p-value is 0.011.Since the p-value is less than significance level (0.05), reject the null hypothesis.Therefore, there is enough evidence to conclude a linear relationship between parent age and litter size. Consider the significance of slope coefficients: where, where The test statistic corresponding to 'age of sire' is -0.6516 and the p-value is 0.529. Since the p-value is greater than 0.05, we fail to reject the null hypothesis. Meaning, there is insufficient evidence to conclude a linear relationship between 'age of sire' and 'litter size'.The test statistic corresponding to 'age of sire' is -3.8327 and the p-value is 0.0033. Since the p-value is less than 0.05, reject the null hypothesis. Meaning, there is sufficient evidence to conclude a linear relationship between 'age of dam' and 'litter size'.The R-square value is 0.5972. Meaning, 59.72% of variation in the litter size is explained by the variation in age of sire and age of dam, that is explained by the model.The equation of the multiple regression model is:The F-statistic is 7.414 and the p-value is 0.011.Reject the null hypothesis. There is enough evidence to conclude a linear relationship between parent age and litter size. Consider the significance of slope coefficients: where, where The test statistic corresponding to 'age of sire' is -0.6516 and the p-value is 0.529. Since the p-value is greater than 0.05, we fail to reject the null hypothesis. Meaning, there is insufficient evidence to conclude a linear relationship between 'age of sire' and 'litter size'.The test statistic corresponding to 'age of sire' is -3.8327 and the p-value is 0.0033. Since the p-value is less than 0.05, reject the null hypothesis. Meaning, there is sufficient evidence to conclude a linear relationship between 'age of dam' and 'litter size'.About 59.72% of variation in the litter size is explained by the variation in age of sire and age of dam, that is explained by the model.

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