The following is an incomplete screenshot of the estimated regression analysis u
ID: 3061124 • Letter: T
Question
The following is an incomplete screenshot of the estimated regression analysis using excel that could be used to estimate the price for a bicycle, given its weight.
Assuming the conditions necessary for valid inference in regression are satisfied, what is the estimated regression model? Test whether each of the regression parameters 0 and 1 is equal to zero at a 0.05 level of significance. What are the correct interpretations of the estimated regression parameters? Are these interpretations reasonable?
SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations 0.929366408 0.86372192 0.84668716 942.2660545 10 ANOVA df MS Significance Regression Residual Total 1 45017877.46 45017877.46 50.70349813 9.99374E-05 8 7102922.539 887865.3174 52120800 Coefficients Standard Errort Stat 28818.00368 3267.256839 1439.00644202.0895123 P-value 2.14888E-0521283.695936352.31146 17855.09147 39780.91589 9.99374E-05-1905.025691 -972.9871886 -2117.095029 -760.9178503 Lower 95% Upper 95% Lower 99.0% Upper 99.0% Intercept WeightExplanation / Answer
Here' the interpretation:
The estimated regression model is
Estimated price of cyce = 28818.00368 - 1439.00644 * Weight
To know wether the coefficients of regression params 0 and 1 are equal to 0 at .05 significance level:
Check the p-value of the Intercept and Weight coefficients. They are much less than .05. Indicating that the hypothesis test for each of these coefficients has resulted in rejection of Ho or B = 0, and hence, the 2 paramaters are statistically significant
> The correct interpreation is Price of the bike decreases by 1439.00644 units per kg increase in the weight of the bike. This is a reasonable interpretation, given the fact that lesser the bike weights, the costlier is the material the bike is made up of. And hence, the pricier the bike is gonna be.
> On intercept, the correct interpretation is for a bike which weights 0 kg price is 28818.00368, which actually is not a reasonable interpretation
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