Construct a linear regression model that predicts the price of houses in a neighborhood in Canton given their area in square feet and their age in years

House price in $1000s	Square Feet	House age (Years)
245	1400	15
312	1600	17
279	1700	13
308	1875	24
199	1100	25
219	1550	20
405	2350	19
324	2450	12
319	1425	14
255	1700	16

(a) Define the design matrix and the true response.

(b) Complete the following tables (Show your work for partial credits). Interpret the results.

	E[Coefficients]	Variance of Coefficients
Intercept
Square Feet
House age

	df	SS	MS
Regression
Residual
Total

R Squared
Adjusted R Squared
AIC
Standard Error
Number of Observations

(c) Construct proper hypothesis tests to identify the factors that significantly change (statistically) the house price.

(d) Find the expected values and prediction intervals for the following:

Square Feet	House age (Years)	Expected Price	Lower Prediction bound	Upper Prediction bound
1700	13
2400	17
4000	5

(e) Interpret the results in the table above.

(f) Check and discuss the potential of multicollinearity between your input factors.