Consider splitting the response values y 1 y n into

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Problem 3Consider splitting the response valuesy1, . . . , yninto two groups with respective sample sizesn1andn2. Define thedummyvariable(1)xi=(1if group one0if group twoShow that the least squares estimators ofβ1andβ0are respectivelyˆβ1= ¯y1-¯y2andˆβ0= ¯y2,where ¯y1and ¯y2are the respective sample means of each group.Problem 4Fusible interlinings are being used with increasing frequency to support outer fabrics andimprove the shape and drape of various pieces of clothing.The articleCompatibility ofOuter and Feasible Interlining Fabrics in Tailored Garmentsgave the accompanying dataon extensibility (%) at 100 gm/cm for both high-quality (H) fabric and poor-quality (P)fabric specimens.H1.2.9.71.01.71.71.1.91.71.91.32.11.61.81.41.31.91.6.82.01.71.62.32.0P1.61.51.12.11.51.31.02.6UseRto perform the following tasks.i. Create an appropriate graphic to visualize the relationship between extensibility andquality. Do you think there is a relationship between extensibility and quality? Makesure to label the plot.ii. Using the indicator variablex=(1if high quality0if low qualityrun a regression analysis to test if the average fabric extensibility differs per group.3

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