12. Agriculture researchers wished to see if they could obtain a linear regressi
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Question
12. Agriculture researchers wished to see if they could obtain a linear regression equation that could be used to predict the yield of a certain crop. For a random sample of 15 plots of the crop, they obtained data on yield, a measure of insect infestation, and a measure of soil quality. The results were as follows SUMMARY OUTPUT Regression Statistics 0.91391427 Multiple R R Square 0.83523928 Adjusted R Square 0.80777917 2.00720133 Standard Error Observations 15 ANOVA df SS MS Significance F Regression 245.087 122.5435 30.41645 2.00042E-05 Residual 12 48.34629 4.028857 14 293.4333 Total Coefficients Std. Error t Stat P-value Lower 95% r 95% 11.2977 80.5688 Intercept 45.9332 15.8965 2.89 0.0136 2.4033 7.8626 5.1330 1.2528 4.10 0.0015 soilqual -1.1256 0.1095 insects 0.5081 0.2834 1.79 0.0983 a) According to the output, if the level of insect infestation is decreased by one unit and soil quality is held constant, will predicted yield increase or decrease? By how much will it change? b Construct a 95% confidence interval around the coefficient for soil quality. c) Test whether the insect infestation coefficient is different from 0 at the significance level of0.10. Report the p-value and your conclusion about the coefficient.Explanation / Answer
Here in 12b ,we have to find the confidence interval i.e. the range of values which will the give the good estimates of the population parameter. Hence we see The range of the observed values of the test statistic which are close to the tabulated value of the test statistic. This tabulated value is obtained from the biometrica table ,not from the observed data here and this value gives the standard value of the test statistic, independent of the parameters.
In 12c to calculate the p value we use P[T>=to| Ho] , where The is the test statistic and to is the observed value of the test statistic, obtained from the data.
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