One factor that influences the cost of a 3D television is its size. The following data represent the size and price for a random sample of 3D televisions of varying brands and models.

(a) Draw a scatter diagram of the data using size as the explanatory variable.

(b) Determine the linear correlation coefficient between the size and price. 

(c) Does a linear relation exist between size and price?

(d) Find the least-squares regression line treating size as the explanatory variable.

(e) Interpret the slope.

(f) Is it reasonable to interpret the intercept? Explain.

(g) What proportion of variability in price is explained by the variability in size?

(h) Determine estimates for β₀ and β₁.

(i) Compute the standard error of the estimate.

(j) Determine whether the residuals are normally distributed.

(k) Determine sβ₁.

(l) Assuming residuals are normally distributed, test whether a linear relation exists between size and price at the a = 0.05 level of significance.

(m) Assuming residuals are normally distributed, construct a 95% confidence interval for the slope of the true least squares regression line.
(n) Predict the mean price of 52-inch 3D televisions.

(o) Construct a 95% confidence interval about the mean price of 52-inch televisions.

(p) Is the price of the 52-inch Sharp 3D television above or below the average price for 52-inch 3D televisions?

(q) Predict the price of a randomly selected 52-inch 3D television.

(r) Construct a 95% prediction interval for the price a 52-inch 3D television.

(s) In part (g), you found the proportion of variability in price that is explained by the variability in size. What lurking variables might also have an effect on price?

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Price ($) Size (in.) Brand/Model Sony Bravia KDL-40HX800 40 1168 Samsung UN40C7000WF 40 1170 Samsung UN46C7000 46 1494 Sony Bravia 46HX800 46 1500 Samsung UN46C8000 46 1559 Sharp LC52LE925UN 52 2700 Samsung UN55C7000WF Sony Bravia XBR-60LX900 55 2600 60 3890 Panasonic Viera TC-P65VT25 65 4478