Suppose you estimate the following the degree to which HDTV sales (in millions of units)are related to price,consumer income,and a time-trend as (p-values in parentheses)

$$\begin{array} { lllll }
HD\widehat {TV~ S}ales _ { t } =& 15.43 -& 0.168 \text {Price} +& 0.247 \text {Income } +& 3.52 \text {Time Trend }\
& ( 0.023 )& ( 0.102 ) & ( 0.028 )& ( 0.046 ) \

\end{array}$$
You should conclude that the data do
A)not exhibit a time-trend because the estimated coefficient for Price is not statistically significant.
B)exhibit a time-trend because the estimated coefficient for Income is positive and statistically significant.
C)not exhibit a time-trend because the estimated coefficient for the Time Trend is positive.
D)exhibit a time-trend because the estimated coefficient for the Time Trend is statistically significant.

Question

Suppose you estimate the following the degree to which HDTV sales (in millions of units)are related to price,consumer income,and a time-trend as (p-values in parentheses)

$$\begin{array} { lllll } 
HD\widehat {TV~ S}ales  _ { t } =& 15.43 -& 0.168   \text {Price} +& 0.247  \text {Income } +& 3.52  \text {Time Trend }\
& ( 0.023 )&  ( 0.102 ) &  ( 0.028 )& ( 0.046 ) \

\end{array}$$
You should conclude that the data do
A)not exhibit a time-trend because the estimated coefficient for Price is not statistically significant.
B)exhibit a time-trend because the estimated coefficient for Income is positive and statistically significant.
C)not exhibit a time-trend because the estimated coefficient for the Time Trend is positive.
D)exhibit a time-trend because the estimated coefficient for the Time Trend is statistically significant.

Quizplus · Accepted Answer

The best choice is D because the estimated coefficient for the Time Trend is statistically significant at the 5% level of significance (p-value = 0.046). This suggests that there is a significant increase in HDTV sales over time. The estimated coefficients for Price and Income are not statistically significant at the 5% level, meaning that price and consumer income do not have a significant impact on HDTV sales. Therefore, choices A and B are incorrect. Choice C is also incorrect because the positive coefficient for Time Trend alone does not necessarily indicate a time-trend. The statistical significance of the coefficient is important in determining whether or not there is a significant trend over time.

Suppose You Estimate the Following the Degree to Which HDTV