between weight gain (grams) and anount of lysine ingested (gams). The anount of

Question

between weight gain (grams) and anount of lysine ingested (gams). The anount of ysine ingested is the explanatory variable (x) and the weight gain() ia the response variable. The mean of the explanatory variable is o.166. A 1inear regression model ?as fitted to answers to three decinal places necessary examine the relationship the data. The resuits are shown below. Round all Regression Analysis weight gain versus lysine Ingested 128.3579 28,357 26.52 0.000 lysine sngese 1 .3579 20. 3529 26. .40 -4350 Model ?:mary 1.03403 a yane ingested 3s.03 6. .15 0.000 1.0 a. Lysine ingested ranges from .09 to .23 grams. What is the predicted weight gain for .20 grans of lysine ingested? b. Consider a hypothesis test HoA-O vs H.:A.0. what is the p-value for the test? Conclusion: There c. What is the Pearson correlation coefficient? (is/is not) sufficient evidence to conclude B, is not d. What is the 958 prediction interval for an individual y-value at x .20

Explanation / Answer

Sol:

Here dependent variable is weight gain and independent variable is lysine ingested.

Given that mean of X = 0.166

From the given output the regression equation is,

Y = 12.51 + 35.63*x

Now here we have to find y when x = 0.20

Y = 12.51 + 35.63*0.20 = 19.636

Now here we have to test,

H0 : B1 = 0      Vs         H1 : B1 not= 0

Where B1 is population slope for independent variable.

Assume alpha = level of significance = 5% = 0.05

The test statistic = 5.15

P-value = 0.000

P-value < alpha

Reject H0 at 5% level of significance.

Conclusion : There is sufficient evidence to say that B1 is not 0.

Pearson correlation coefficient = sqrt(Rsq) = sqrt(72.62%) = sqrt(0.7262)

Correlation = 0.8522

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