95% prediction interval is,

1. Expected sales for sentiment index 90

95% prediction interval

• Expected sales for sentiment index 100

95% prediction interval

Answer 2

1. 
   
   

• 
  

The equation is,

• 
  
  

Answer 3

Here a regression model is given to predict the Diet Partners’ portfolio return (in percent) in terms of its management fee (in percent). The equation is,

RETURN=-3.021+7.062 (FEE)

1. The predicted RETURN if FEE is 0 percent,

RETURN₀=-3.021

The predicted RETURN is FEE is 1 percent,

RETURN₁=-3.021+7.062=4.041

• The relationship between RETURN and FEE is examined by conducting a two-tailed test. The hypotheses are,

Null hypothesis: there is no significant association between RETURN and FEE.

Alternative hypothesis: RETURN is significantly related to FEE.

The level of significance is considered as 0.05. The value of the t-statistic associated with FEE is 14.95. The p-value is 0.04252<0.05. Hence the null hypothesis is rejected at 5% level and it is concluded that there is a significant relationship between RETURN and FEE.

• The coefficient of determination is 0.794 which means 79.4% variability in RETURN can be explained by the regression model. Also the slope coefficient for FEE shows that for one percent increment in FEE, the return will be increased by 7.062 percent. Therefore Smith would be justified in concluding that the high fees are good for clients.

Answer 4

Regression Statistics
Multiple R	0.236885
R-squared	0.056114
Standard errors	0.158926
Observations	1819
ANOVA	df	SS	MSS	F	Significance F
regression	1	14.246	14.246	564.029	0
Residual	1817	45.893	0.025
Total	1818	60.139
	Coefficient	Standard error	T-stat	p-value	Lower 98%	Upper 98%
Intercept	0.55851	0.018707	29.8554	0	0.52182	0.5952
Slope coefficient	-0.04375	0.001842	-23.7514	0	-0.10236	0.014863

 Formulae used: