1. (1.1) Write out the distance-from-core hypothesis, first as a single-tailed research hypothesis of the more probable (positive) relationship between (improving) overall exterior housing quality and (farther) distance from the core in the Glengarry neighbourhood; and then (1.2) second, re-express this as a two-tailed research hypothesis for statistical testing. (1.3) Propose an explanation or theory as to why overall exterior housing quality may improve or deteriorate with farther distance from a core.
2. (2.1) Interpret the meaning of the \({{\beta }_{0\text{ Intercept}}}\)

• Intercept Coefficient as the height of the linear relationship after (2.2) using the formulas to calculate the value of this coefficient from the available statistics.

(3) (3.1) Interpret the meaning of the \[{{\beta }_{1\,\,\text{Slope}}}\]

-slope Coefficient as the orientation of the linear relationship after (3.2) using the formulas to calculate the value of this coefficient from the available statistics.

(4) Explain the use of the substitution method with the intercept and slope coefficients from questions (2) and (3) for (4.1) calculating at least three predicted values of pHQ2011 percentages at selected DDowntown distances. (4.2) Explain their drawing and labelling on the XY-scatterplot to verify the position of the regression line.

(5) Use the Descriptive Statistics box from the Independent-Samples T-Test to write out (5.1) the sample mean, standard deviation, and number of houses with pHQ2011 percentages in the first sample of neighbourhood houses in 2011, and the corresponding sample mean, standard deviation, and number of houses with pHQ2011 percentages in the second sample of neighbourhood houses in 2011. (5.2) Describe differences between "near-to-core" and "far-from-core" sample means, standard deviations, and numbers of houses. (5.3) Summarize from question (1) a research hypothesis based upon a theory about why a house's overall exterior quality may improve or deteriorate with farther distance from a core; and then nullify this for a null hypothesis.

(6) (6.1) Explain how observed Tabs comparing near-to-core and far-from-core samples' pHQ2011 mean percentages is calculated in the Independent-Samples T-Test. (6.2) Use the alpha significance level of this observed Tabs to decide whether to reject a null hypothesis of no average difference-with-distance at or below a conventional level of statistical significance. (6.3) In conclusion, interpret the meaning of the result for the proposed research hypothesis in questions (1) and (5.3).

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