(By-Hand) A dietetics student wants to look at the relationship between calcium intake (g/week) and knowledge score about calcium in sports science students (knowledgescore out of 50). Further she wants to know if knowledge about calcium can be used to predict calcium intake of the students. The table below shows the data she collected.Knowledge Score38Total:DENFES254828224118263043319Calcium Intake9.407.339.857.635.838.107.987.748.0510.8582.76xy357.20183.25472.80213.64128.26332.10143.64201.24241.50466.552740.2x²144462523047844841681324676900184911071y²88.360053.728997.022558.216933.988965.610063.680459.907664.8025117.7225703.0402 Part d:Compute the least squares regression equation. Show your work.Parte:If appropriate, use a 99% interval for the average calcium intake of people who have a knowledge score of 3 (show your work). If not appropriate, explain why. Eitherway, clearly present your answer in a sentence. [Hint: Use the key words to determine if this should be a confidence interval or a prediction interval.]Part f:If appropriate, use a 99% interval for the specific calcium intake of Darby Alexander who have a knowledge score of 41 (show your work). If not appropriate, explain why.Either way, clearly present your answer in a sentence. [Hint: Use the key words to determine if this should be a confidence interval or a prediction interval.]

The given data is Knowledge Score Calcium Intake xy x2 y2 38 9.4 357.2 1444 88.36 25 7.33 183.25 625 53.7289 48 9.85 472.8 2304 97.0225 28 7.63 213.64 784 58.2169 22 5.83 128.26 484 33.9889 41 8.1 332.1 1681 65.61 18 7.98 143.64 324 63.6804 26 7.74 201.24 676 59.9076 30 8.05 241.5 900 64.8025 43 10.85 466.55 1849 117.7225 Sum 319 82.76 2740.2 11071 703.0402 From the given data, we have n=10,∑x=319,∑y=82.76,∑xy=2740.2,∑x2=11071,∑y2=703.0402.d) The least squares regression equation is y^=b0+b1x, where b0=y¯-b1×x¯ and b1=∑(x-x¯)(y-y¯)∑(x-x¯)2. Now, x¯=∑xn=31910=31.9 y¯=∑yn=82.7610=8.276 b1=∑(x-x¯)(y-y¯)∑(x-x¯)2=∑xy-n×x¯×y¯∑x2-n×x¯2=2740.2-10×31.9×8.27611071-10×(31.9)2≈0.1119 b0=y¯-b1×x¯=8.276-0.1119×31.9≈4.7064 So, the least squares regression equation is y^=4.7064+0.1119x.e) Here if appropriate, we construct a 99% interval for the average calcium intake of people who have a knowledge score of 3. So, this is the confidence interval for the mean value of y corresponding to x=3. In this problem, the range of the given x-values is from 18 to 48. Note that x=3 is outside the range of the x-values. We know that the estimated mean value of y corresponding to a particular value of x will be highly unreliable if that value of x is outside the range of the given x-values. So, here, the estimated average calcium intake of people who have a knowledge score of 3 is highly unreliable. So, it is not appropriate to use a 99% interval for the average calcium intake of people who have a knowledge score of 3.f) Here if appropriate, we construct a 99% interval for the specific calcium intake of Darby Alexander who has a knowledge score of 41. So, this is the prediction interval for the predicted value of y corresponding to x=41. Note that x=41 is inside the range of the given x-values. So, it is appropriate to use a 99% interval for the specific calcium intake of Darby Alexander who has a knowledge score of 41. A 100×(1-α)% prediction interval for the predicted value of y corresponding to a value x=x* is y^*-E,y^*+E, where E=tα2;(n-2)×se×1+1n+x*-x¯2SSxx and α=1-confidence level. Now, SSxx=∑x-x¯2=∑x2-n×x¯2=11071-10×(31.9)2 =894.9 SSyy=∑y-y¯2=∑y2-n×y¯2=703.0402-10×(8.276)2 =18.11844 SSxy=∑x-x¯y-y¯=∑xy-n×x¯×y¯=2740.2-10×31.9×8.276=100.156The standard error of estimate is se=SSyy-SSxy2SSxxn-2=18.11844-(100.156)2894.910-2≈0.9293 Now, α=1-0.99=0.01 So, tα2;(n-2)=t0.012;(10-2)≈3.355 We use excel to find t0.012;(10-2).The predicted value of y corresponding to x=41 is y^*=4.7064+0.1119×41=9.2943 The margin of error is E=tα2;(n-2)×se×1+1n+x*-x¯2SSxx=3.355×0.9293×1+110+41-31.92894.9≈3.4047 So, a 99% prediction interval for the predicted value of y corresponding to x=41 is y^*-E,y^*+E=(9.2943-3.4047,9.2943+3.4047)≈(5.89,12.70) A 99% interval for the specific calcium intake of Darby Alexander who has a knowledge score of 41 is (5.89,12.70).