In a certain type of metal test specimen, the normal stress on a specimen is known to be functionally related to shear resistance

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In a certain type of metal test specimen, the normal stress on a specimen is known to be functionally related to shear resistance. The following is a set of coded experimental data on the two variables. Read the data provided in the table above, into Ras two vectors. Produce an appropriate plot to observe the linear relationship between the two variables. Produce an appropriate linear regression model in R, for the data provided. Normal Stress, X Shear Resistance, y 26.8 26.5 25.4 27.3 28.9 24.2 23.6 27.1 27.7 23.6 23.9 25.9 24.7 26.3 28.1 22.5 26.9 21.7 27.4 21.4 22.6 25.8 25.6 24.9

a) Using values from your output, write out the estimated linear regression equation.

b) Using an appropriate test statistic from your output, test the pair of hypotheses, Ho: B = 0 versus H: B = 0. You are required to carry out this using the critical value approach at a level of significance of a = 0.05

c) Produce appropriate R code to find a 95% confidence interval for the regression slope coefficient. Paste your code and output in the space provided. Provide an interpretation of this interval.

d) Is the estimated regression equation in (a) suitable for predicting the shear resistance for a normal stress of 24.5? Support your answer with appropriate summary statistics for the variable normal stress. If your answer is yes, find the predicted shear resistance for a normal stress of 24.5.