Problem
\begin{tabular}{|c|c|} \hline $\begin{array}{c}\text { House Price } \\ \text { in } \$ 1000 s \\ (y)\end{array}$ & $\begin{array}{c}\text { Square Feet } \\ (x)\end{array}$ \\ \hline 245 & 1400 \\ \hline 312 & 1600 \\ \hline 279 & 1700 \\ \hline 308 & 1875 \\ \hline 199 & 1100 \\ \hline 219 & 1550 \\ \hline 405 & 2350 \\ \hline 324 & 2450 \\ \hline 319 & 1425 \\ \hline 255 & 1700 \\ \hline \end{tabular} Estimated Regression Equation: house price $=98.25+0.1098$ (sq.ft.) The slope of this model is 0.1098 Does square footage of the house significantly affect its sales price?
Solution
Step 1 ：\(H_0: \beta_1 = 0\) (Square footage does not significantly affect the house price)
Step 2 ：\(H_1: \beta_1 \neq 0\) (Square footage significantly affects the house price)
Step 3 ：Significance level: \(\alpha = 0.05\)
Step 4 ：Calculate the standard error of the slope (SE): \(SE = 0.03297\)
Step 5 ：Calculate the t-statistic: \(t = 3.3304\)
Step 6 ：Calculate the p-value: \(p = 0.0104\)
Step 7 ：\(\boxed{\text{Final Answer: Since the p-value is less than the significance level of 0.05, we reject the null hypothesis. Therefore, the square footage of the house significantly affects its sales price.}}\)
