A group of engineers are investigating how the shear strength of masonry joints

Question

A group of engineers are investigating how the shear strength of masonry joints is related to the age of the joint. Some data are collected and presented in the table below. A linear regression model: y_1 = beta_0 + beta_1 x_i + elementof_1 is proposed for the data. R output from fitting this model to the data is: (a) Interpret the estimated regression coefficient of Age in the context of this study. (b) From the output given, calculate the p-value for the following hypothesis test: H_0: beta_1 = 0 vs. H_A: beta_1

Explanation / Answer

Part-a

Corresponding to one year increase in age there is on an average a decrease of 0.08061 in the shear strength of masonry joints.

Part-b

p-value of test of coefficient of age is p=0.00516/2=0.00258

As p-value<0.05, we reject the null hypothesis and conclude that age has inverse impact on strength

Part-c

Mea shearstrength =5.05707-0.08061*3.5=4.774935

Part-d

Coefficient of determination=0.833 which means that age explained 83.3% of variability in shear strength

Part-e

It is assumed that errors are independent, normally distributed , have zero mean and constant variances

Part-f

Constant variance assumption could be checked by plot of residual versus fitted values. If errors are of constant variance then the plot should be horizontal band and should not have any pattern.

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