Data were collected from a random sample of 390 home sales from a community in 2003. Let:

- Price denote the selling price (in $1,000)
- BDR denote the number of bedrooms
- Bath denote the number of bathrooms
- Hsize denote the size of the house (in square feet)
- Lsize denote the lot size (in square feet)
- Age denote the age of the house (in years)
- Poor denote a binary variable that is equal to 1 if the condition of the house is reported as "poor."

An estimated regression yields:

\[ \text{Price} = 126.4 + 0.514 \times \text{BDR} + 24.8 \times \text{Bath} + 0.165 \times \text{Hsize} + 0.004 \times \text{Lsize} \]
\[ (25.3) \quad (2.56) \quad (9.48) \quad (0.012) \quad (0.00051) \]
\[ + 0.095 \times \text{Age} - 51.7 \times \text{Poor}, \quad R^2 = 0.76, \quad SER = 44.0 \]
\[ (0.330) \quad (11.1) \]

The t-statistic for the coefficient on BDR is 2.01. (Round your response to three decimal places.)

Is the coefficient on BDR statistically significantly different from zero?

A. Since the t-statistic > 0.05, the coefficient on BDR is not statistically significantly different from zero.
B. Since the t-statistic < 1.96, the coefficient on BDR is not statistically significantly different from zero.
C. Since the t-statistic > 1.96, the coefficient on BDR is statistically significantly different from zero.
D. Since the t-statistic < 0.05, the coefficient on BDR is statistically significantly different from zero.

The coefficient on BDR in the regression model is statistically significantly different from zero. This conclusion is based on the given t-statistic of 201 for the coefficient on BDR, which is much larger than the critical value of 1.96 at the 5% significance level. Therefore, we reject the null hypothesis that the coefficient on BDR is zero and conclude that there is a statistically significant relationship between the number of bedrooms (BDR) and the selling price (Price) of the homes. The t-statistic provides evidence that the coefficient on BDR is not likely to be a result of random chance and suggests that an increase in the number of bedrooms has a positive impact on the selling price, holding other variables constant.

In regression analysis, the t-statistic is used to determine the statistical significance of a coefficient estimate. The t-statistic measures the ratio of the estimated coefficient to its standard error. If the t-statistic is larger than a critical value (in this case, 1.96 at the 5% significance level), we can conclude that the coefficient is statistically significantly different from zero.

In this case, the t-statistic for the coefficient on BDR is given as 201, which is much larger than 1.96. This indicates a strong evidence against the null hypothesis that the coefficient on BDR is zero. Therefore, we can conclude that the coefficient on BDR is statistically significantly different from zero, suggesting that the number of bedrooms has a significant impact on the selling price of the homes.

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