STAT-701 MID EXAM MPHIL EDU
Time:90 min
Use Table value 2.5 fort-test and 5 for F-test
Marks: 18
Q.1. The family expenditures (\$1000s) (Y) Income of 12 families \( (\mathrm{X}) \) is given in the side tale. (i) Fit the
\begin{tabular}{|l|l|l|l|l|l|l|l|l|l|l|l|l|}
\hline \( \mathrm{X} \) & 20 & 30 & 33 & 40 & 15 & 13 & 26 & 38 & 35 & 43 & 45 & 50 \\
\hline \( \mathrm{Y} \) & 7 & 9 & 8 & 11 & 5 & 4 & 8 & 10 & 9 & 10 & 12 & 15 \\
\hline
\end{tabular}
appropriate model. (ii) Test the significance of the regression.(iii) Find \( 95 \% \) C.I \( \beta_{1} \) ?
Q.2.The following information has been gathered from a random sample of size 9 from apartment's renters in Faisalabad city the fitted regression model is: \( \hat{Y}=96.4581+136.4847 X_{1}-2.4035 X_{2}, \mathrm{TSS}=335187, \mathrm{SSE}=28277, \mathrm{~S}_{\mathrm{b} 1}=2.5, \mathrm{~S}_{\mathrm{b} 2}=0.5 \), Where \( \mathrm{Y}= \) Rent (Rs.1000), \( \mathrm{X}_{1}= \) Number of Rooms, \( \mathrm{X}_{2}= \) Distance from center point (miles)
(i) Interpret the model parameters. (ii) Predict the rent for a person who looking a house with 3 bedroom and located at 7 miles from center point.(iii) Test for a significant relationship among \( X_{1}, X_{2} \) and \( Y \). use \( \alpha=0.05 \). (iv) Is distance of a house from central point have a significant effect on rent at \( \alpha=5 \% \). (v) Find Coefficient of determination and interpret.
Q.3.(a) The following model is show the relationship between sales \( (Y) \) and months employed \( (X) \). \( \hat{y}=42+6.34 X-0.04 X^{2} \) and \( \mathrm{R} 2=0.902, \mathrm{TSS}=14244 \) and \( \mathrm{Sb} 1=1.5 \mathrm{Sb} 2=0.005 \) (i) Test the significance of Quadratic term. (ii) Test the overall significance of regression (11i) Find the months employed that maximizes the sale also find \( { }^{2} \) the maximum Sale. F-tuble
(b) The simple correlation coefficients of 10 observations between \( X_{1} \) and \( X_{2} \) is \( 0.80, X_{1} \) and \( X_{3}^{2} \) is \( 0.85, X_{2} \) and \( Y^{\frac{-b}{4 h}} \). 0.95, Test the significance of \( \rho_{23}=0 \).
() \( r_{12}=\frac{5 x^{2} y}{\sqrt{s^{2}-5 y^{2}}} \quad \gamma_{12}-\gamma_{73}, \gamma_{23} \)
