$20.$ Electromagnetic technologies such as ground pen$$ etrating radar offer effective nondestructive sensing techniques to determine a continuous profile of a pavement structure. The propagation of electromag$$ netic waves through the structure depends critically on the dielectric properties of the media. However, little research has been done on the characteriza$$ tion of dielectric properties of asphalt mixtures. The article $$Dielectric Modeling of Asphalt Mixtures and Relationship with Density$($J$.$ Transp. Engr., $2011$: $104111)$ reported on the dielectric response with percent air voids for various asphalt mixtures at $7$GHz frequency. The following data, kindly pro$$ vided by the authors of the cited article, compares y$=$dielectric constant and x$=$air void $(\%)$ for $18$ samples having $5\%$ asphalt content:

y: $4\mathrm{.}554\mathrm{.}494\mathrm{.}504\mathrm{.}474\mathrm{.}474\mathrm{.}45$

x: $4\mathrm{.}354\mathrm{.}795\mathrm{.}575\mathrm{.}205\mathrm{.}075\mathrm{.}79$

y: $4\mathrm{.}404\mathrm{.}344\mathrm{.}434\mathrm{.}434\mathrm{.}424\mathrm{.}40$

x: $5\mathrm{.}366\mathrm{.}405\mathrm{.}665\mathrm{.}906\mathrm{.}495\mathrm{.}70$

y: $4\mathrm{.}334\mathrm{.}444\mathrm{.}404\mathrm{.}264\mathrm{.}324\mathrm{.}34$

x: $6\mathrm{.}496\mathrm{.}376\mathrm{.}517\mathrm{.}886\mathrm{.}747\mathrm{.}08$

a$.$ Does a scatterplot of the data suggest it is reason$$ able to assume an approximate linear relation$$ ship between x and y$?$

b$.$ Find the equation of the least squares line for this data and interpret its slope.

c$.$ Determine the proportion of observed variation in the response variable that can be attributed to the approximate linear relationship between strength and fiber weight.

d$.$ Does a residual plot indicate any deficiency in a straight line fit? Explain your reasoning.